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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-07-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000078890</issuerCik>
        <issuerName>BRINKS CO</issuerName>
        <issuerTradingSymbol>BCO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001434591</rptOwnerCik>
            <rptOwnerName>SCHUMACHER MATTHEW AP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1801 BAYBERRY COURT</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 18100</rptOwnerStreet2>
            <rptOwnerCity>RICHMOND</rptOwnerCity>
            <rptOwnerState>VA</rptOwnerState>
            <rptOwnerZipCode>23226</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Controller</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-07-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5539</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19051</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Subject to the terms and conditions of the 2005 Equity Incentive Plan and a Restricted Stock Units Award Agreement, the Reporting Person has been granted Restricted Stock Units and shall be entitled to receive following the relevant vesting date the number of shares of The Brink's Company's common stock underlying the Resticted Stock Units subject to vesting as follows: 1,847 shares on July 11, 2013 and 1,846 shares on each of July 11, 2014 and 2015.</footnote>
        <footnote id="F2">Includes 8,556 Restricted Stock Units that have not yet vested.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Elizabeth C. Restivo,
Elizabeth C. Restivo, Attorney-in-Fact</signatureName>
        <signatureDate>2012-07-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
