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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-10-07</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"/>
            </securityTitle>
            <transactionDate>
                <value>2019-10-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1265250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3578560</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>2019-10-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>497876</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.37</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3080684</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Ordinary Shares may be represented by American Depositary Shares, each of which currently represents one Ordinary Share.</footnote>
        <footnote id="F2">In January 2015, 2,530,500 restricted stock units (the &quot;RSUs&quot;) were approved to be granted and, following the Annual General Meeting of Shareholders held in July 2015, were granted to the Reporting Person under the Amarin Corporation plc 2011 Stock Incentive Plan (the &quot;Plan&quot;). Each RSU represents a contingent right to receive one Ordinary Share or cash in lieu thereof at the Issuer's discretion. The RSUs vested in two equal installments based on the Issuer's satisfaction of certain performance criteria and continued employment of the Reporting Person as provided in the Restricted Stock Unit Award Agreement between the Issuer and the Reporting Person. Vesting of the second and final installment was achieved based on a predetermined performance-based formula tied to company cash flow as determined by the Remuneration Committee of the Board of Directors, resulting in the vesting of 1,265,250 RSUs.</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">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>
    </footnotes>

    <remarks>As of the date of this Form 4, the Reporting Person owns or holds the right to acquire an aggregate of 9,707,117 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 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>2019-10-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
