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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001408920</rptOwnerCik>
            <rptOwnerName>Kennedy Joseph T</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2016-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>47188</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>209308</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2016-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6250</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>215558</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2016-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>27885</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.08</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>187673</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>47188</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>47188</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>471874</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6250</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>62500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Ordinary Shares may be represented by American Depositary Shares, each of which represents one Ordinary Share.</footnote>
        <footnote id="F2">As previously reported on July 8, 2015, the Reporting Person was granted 755,000 Restricted Stock Units (&quot;RSUs&quot;) under the Amarin Corporation plc 2011 Stock Incentive Plan. These RSUs vest in 16 equal quarterly installments. The sixth vesting event occurred on December 31, 2016.</footnote>
        <footnote id="F3">Not applicable.</footnote>
        <footnote id="F4">Please see the section titled &quot;Remarks&quot; below for additional information.</footnote>
        <footnote id="F5">As previously reported on October 6, 2015, the Reporting Person was granted 100,000 RSUs under the Plan. These RSUs vest in 16 equal quarterly installments. The sixth vesting event occurred on December 31, 2016.</footnote>
        <footnote id="F6">Represents withholding by the Issuer of shares in respect of tax liability incident to the vesting of a security issued in accordance with Rule 16b-3, and not a market sale of securities.</footnote>
        <footnote id="F7">Each RSU represents a contingent right to receive one Ordinary Share or cash in lieu thereof at the Issuer's discretion.</footnote>
    </footnotes>

    <remarks>In the event of a Change of Control (as defined in the Plan), the grants described in this Form 4 vest in full.

As of the date of this Form 4, the Reporting Person owns or holds the right to acquire an aggregate of 3,396,922 Ordinary Shares of the Issuer in the form of (i) stock options and Restricted Stock Units granted under the Amarin Corporation plc 2002 Stock Option Plan and the Amarin Corporation plc 2011 Stock Option Plan and (ii) 187,673 Ordinary Shares.</remarks>

    <ownerSignature>
        <signatureName>/s/ Joseph T. Kennedy</signatureName>
        <signatureDate>2017-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
