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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-04-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001397144</rptOwnerCik>
            <rptOwnerName>Abingworth LLP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PRINCE HOUSE</rptOwnerStreet1>
            <rptOwnerStreet2>38 JERMYN STREET</rptOwnerStreet2>
            <rptOwnerCity>LONDON</rptOwnerCity>
            <rptOwnerState>X0</rptOwnerState>
            <rptOwnerZipCode>SW1Y 6DN</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, 50 pence par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2012-04-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2300000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5607509</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Notes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Abingworth LLP (the &quot;Reporting Person&quot;) is the investment manager to a number of investment funds that include Abingworth Bioventures V L.P. (&quot;ABV V&quot;), Abingworth Bioventures V Co-Invest Growth Equity Fund LP (&quot;AGE&quot;), and Abingworth Bioequities Master Fund Limited (&quot;ABE,&quot; and collectively with ABV V and AGE, the &quot;Abingworth Funds&quot;).  On April 3, 2012, ABV sold an aggregate of 1,000,000 ordinary shares, 50 pence par value per share, of Amarin Corporation plc (&quot;Ordinary Shares&quot;), AGE sold an aggregate of 1,000,000 Ordinary Shares, and ABE sold an aggregate of 300,000 Ordinary Shares.</footnote>
        <footnote id="F2">The Reporting Person may be deemed to beneficially own the Ordinary Shares reported herein indirectly through the Abingworth Funds.  The Reporting Person's interest in the securities reported herein is limited to the extent of its pecuniary interest, if any, in the Abingworth Funds.  This report shall not be deemed an admission that the Reporting Person, each Abingworth Fund or any other person is the beneficial owner of the securities reported herein for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John Heard, Authorized Signatory</signatureName>
        <signatureDate>2012-04-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
