<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-11-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000897448</issuerCik>
        <issuerName>AMARIN CORP PLC\UK</issuerName>
        <issuerTradingSymbol>AMRN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001199637</rptOwnerCik>
            <rptOwnerName>THERO JOHN F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AMARIN PHARMA, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>1430 ROUTE 206</rptOwnerStreet2>
            <rptOwnerCity>BEDMINSTER</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07921</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>407611</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.35</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2702139</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>136422</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.0498</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2565717</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>244031</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.0273</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2321686</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>222158</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.7096</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2099528</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>20.722</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2094528</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.35</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>407611</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2019-12-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>407611</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option exercise and sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the Reporting Person established in 2017.  The option reported in this Form 4 was granted in 2009 and was set to expire in 2019.</footnote>
        <footnote id="F2">The Ordinary Shares may be represented by American Depositary Shares, each of which currently represents one Ordinary Share.</footnote>
        <footnote id="F3">Please see the section titled &quot;Remarks&quot; below for additional information.</footnote>
        <footnote id="F4">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $17.43 to $18.42, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff at the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F5">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $18.43 to $19.42, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff at the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F6">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $19.43 to $20.41, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff at the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F7">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $20.46 to $20.98, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff at the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F8">On December 21, 2009, the Reporting Person was granted an option to purchase 900,000 Ordinary Shares under the Amarin Corporation plc 2002 Stock Option Plan. The stock option is fully vested.</footnote>
    </footnotes>

    <remarks>As of the date of this Form 4, the Reporting Person owns or holds the right to acquire an aggregate of 10,123,841 Ordinary Shares of the Issuer in the form of Ordinary Shares, stock options and Restricted Stock Units granted under the Amarin Corporation plc 2002 Stock Option Plan and the Amarin Corporation plc 2011 Plan.</remarks>

    <ownerSignature>
        <signatureName>/s/ John F. Thero</signatureName>
        <signatureDate>2018-11-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
