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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-12-20</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, 38 JERMYN STREET</rptOwnerStreet1>
            <rptOwnerStreet2></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>2011-12-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>11683</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7907509</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Notes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.03</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-02-10</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7200</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>96000</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Notes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Joseph Anderson, a partner of Abingworth LLP (the &quot;Reporting Person&quot;), has been issued, to date, an aggregate of 11,683 ordinary shares, 50 pence par value per share (&quot;Ordinary Shares&quot;), of Amarin Corporation plc (the &quot;Issuer&quot;), in consideration of his services as a director of the Issuer. The Reporting Person 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 (collectively, the &quot;Abingworth Funds&quot;). Under an agreement entered into between Mr. Anderson and the Reporting Person on December 20, 2011, Mr. Anderson is deemed to hold all of these 11,683 Ordinary Shares (the &quot;Abingworth Shares&quot;) on behalf of the Reporting Person for the benefit of the Abingworth Funds (specifically, 5,842 Ordinary Shares are held for the benefit of ABV V and 5,841 Ordinary Shares are held for the benefit of AGE).</footnote>
        <footnote id="F2">As previously reported, Mr. Anderson was granted an option on February 20, 2010 (the &quot;Grant Date&quot;) to purchase 120,000 Ordinary Shares under the Amarin Corporation plc 2002 Stock Option Plan in consideration of his services as a director of the Issuer. Under a prior agreement between Mr. Anderson and the Reporting Person, Mr. Anderson was deemed to hold 103,200 of the 120,000 Ordinary Shares underlying the option for the benefit of ABV V and AGE (51,600 ordinary shares each). Pursuant to an agreement between Mr. Anderson and the Reporting Person entered into on December 20, 2011, Mr. Anderson is now deemed to hold 96,000 of the 120,000 Ordinary Shares underlying the option (the &quot;Abingworth Options&quot;) for the benefit of ABV V and AGE (48,000 Ordinary Shares each) and must exercise the Abingworth Options solely upon the direction of the Reporting Person.</footnote>
        <footnote id="F3">The stock option granted to Mr. Anderson initially was scheduled to vest in four equal installments on each anniversary of the Grant Date. However, in light of the Issuer's announcement of favorable data relating to certain of its clinical trials, the Issuer's board of directors approved the acceleration of the vesting schedule relating to certain options (including Mr. Anderson's options) granted by the Issuer, so that all of the vesting dates have been accelerated by a period of six months.</footnote>
        <footnote id="F4">The Reporting Person, on behalf of ABV V or AGE, as applicable, is entitled to direct the disposition of the Abingworth Shares and to receive any proceeds received in connection with the sale or disposition of the Abingworth Shares, and is entitled to the Ordinary Shares issuable upon exercise of the Abingworth Options. The Reporting Person holds the reported securities 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>2011-12-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
