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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-04</periodOfReport>

    <notSubjectToSection16>false</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>true</isDirector>
            <isOfficer>true</isOfficer>
            <isTenPercentOwner>false</isTenPercentOwner>
            <isOther>false</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2020-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>false</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>200000.00</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.9935</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2480441.00</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The sale reported in this Form 4 was 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, pursuant to a Rule 10b5-1 trading plan previously adopted in 2017 by the Reporting Person, in multiple transactions at prices ranging from $15.74 to $16.14, 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>
    </footnotes>

    <remarks>As of the date of this Form 4, the Reporting Person owns or holds the right to acquire an aggregate of 9,556,404 Ordinary Shares of the Issuer in the form of Ordinary Shares, stock options and RSUs granted under the Plan, including but not limited to certain performance-based RSUs that are earned only if product revenues reach pre-defined annual milestone levels and, in certain cases, 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>2020-03-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
