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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-11-11</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>440 US HIGHWAY 22</rptOwnerStreet2>
            <rptOwnerCity>BRIDGEWATER</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>08807</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>2019-11-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>433805</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.0518</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2658480</value>
                    <footnoteId id="F4"/>
                </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>2019-11-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>41741</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.8792</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2616739</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan previously adopted in 2017 by the Reporting Person in accordance with the requirements for such plans described in the Company's Annual Report on Form 10-K.</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">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $16.72 to $17.69, 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="F4">Please see the section titled &quot;Remarks&quot; below for additional information.</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 $17.72 to $17.975, 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>
    </footnotes>

    <remarks>As of the date of this Form 4, the Reporting Person owns or holds the right to acquire an aggregate of 9,231,571 Ordinary Shares of the Issuer in the form of Ordinary Shares, stock options and RSUs granted under the Amarin Corporation plc 2002 Stock Option Plan and the Amarin Corporation plc 2011 Stock Incentive Plan, including but not limited to certain performance-based Restricted Stock Units that are earned only if product revenues reach pre-defined annual milestone levels, then vest only if the recipient remains with the company for an extended period of time.</remarks>

    <ownerSignature>
        <signatureName>/s/ John F. Thero</signatureName>
        <signatureDate>2019-11-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
