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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-06-12</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001022575</issuerCik>
        <issuerName>GOVERNOR &amp; CO OF THE BANK OF IRELAND</issuerName>
        <issuerTradingSymbol>IRE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001026610</rptOwnerCik>
            <rptOwnerName>ROSS WILBUR L JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>319 CLEMATIS STREET</rptOwnerStreet1>
            <rptOwnerStreet2>ROOM 1000 (10TH FLOOR)</rptOwnerStreet2>
            <rptOwnerCity>WEST PALM BEACH</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33401</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Stock, Nominal Value 0.05 Euro each</value>
            </securityTitle>
            <transactionDate>
                <value>2014-06-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1793818229</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.265</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Stock, Nominal Value 0.05 Euro each</value>
            </securityTitle>
            <transactionDate>
                <value>2014-06-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.265</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects the sale of units of Ordinary Stock of the issuer consisting of 1,355,338,135 units sold by WLR Recovery Fund IV, L.P. (&quot;Fund IV&quot;), 312,899,989 units sold by WLR Recovery Fund V, L.P. (&quot;Fund V&quot;), 120,561,272 units sold by WLR/GS Master Co-Investment L.P. (the &quot;Co-Invest Fund&quot;), 5,018,519 units sold by WLR IV Parallel ESC, L.P. (&quot;Parallel Fund IV&quot;) and 314 units sold by WLR V Parallel ESC, L.P. (&quot;Parallel Fund V&quot;) on June 12, 2014.</footnote>
        <footnote id="F2">Notwithstanding the &quot;$&quot;, the sale price listed above is in Euros.</footnote>
        <footnote id="F3">The reporting person is the president and chief executive officer of WL Ross &amp; Co. LLC, the managing member of El Vedado, LLC and the chairman and president of Invesco Private Capital, Inc. El Vedado, LLC is the general partner of WL Ross Group, L.P., which in turn is the managing member of WLR Recovery Associates IV LLC, WLR Recovery Associates V LLC and WLR Master Co-Investment GP, LLC. WLR Recovery Associates IV LLC is the general partner of Fund IV, WLR Recovery Associates V LLC is the general partner of Fund V and WLR Master Co-Investment GP, LLC is the general partner of the Co-Invest Fund. WL Ross &amp; Co. LLC serves as the investment manager to Fund IV, Fund V and the Co-Invest Fund. Invesco Private Capital, Inc. is the managing member of INVESCO WLR IV Associates LLC, which in turn is the general partner of Parallel Fund IV.</footnote>
        <footnote id="F4">INVESCO WLR IV Associates LLC and WLR Recovery Associates IV LLC have entered into a parallel investment agreement pursuant to which WLR Recovery Associates IV LLC has been appointed as representative and attorney of Parallel Fund IV to, among other things, exercise all rights, powers and privileges with respect to the Ordinary Stock owned by Parallel Fund IV and to take whatever action, including voting such Ordinary Stock, as WLR Recovery Associates IV LLC in its discretion deems fit.</footnote>
        <footnote id="F5">Invesco Private Capital, Inc. is also the managing member of INVESCO WLR V Associates LLC, which in turn is the general partner of Parallel Fund V. INVESCO WLR V Associates LLC and WLR Recovery Associates V LLC have entered into a parallel investment agreement pursuant to which WLR Recovery Associates V LLC has been appointed as representative and attorney of Parallel Fund V to, among other things, exercise all rights, powers and privileges with respect to the Ordinary Stock owned by Parallel Fund V and to take whatever action, including voting such Ordinary Stock, as WLR Recovery Associates V LLC in its discretion deems fit.</footnote>
        <footnote id="F6">Reflects the sale of 1,000 units of Ordinary Stock of the issuer by Wilbur L. Ross, Jr. on June 12, 2014.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2014-06-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
