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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2024-01-02</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001671927</issuerCik>
        <issuerName>Immunocore Holdings plc</issuerName>
        <issuerTradingSymbol>IMCR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001969524</rptOwnerCik>
            <rptOwnerName>Coy Travis Alan</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O IMMUNOCORE HOLDINGS PLC</rptOwnerStreet1>
            <rptOwnerStreet2>92 PARK DRIVE, MILTON PARK</rptOwnerStreet2>
            <rptOwnerCity>ABINGDON, OXFORDSHIRE</rptOwnerCity>
            <rptOwnerState>X0</rptOwnerState>
            <rptOwnerZipCode>OX14 4RY</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>No securities beneficially owned.
Exhibit List - Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Travis A. Coy</signatureName>
        <signatureDate>2024-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
