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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001451824</rptOwnerCik>
            <rptOwnerName>Herling Michael J</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>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Brink's Units (DSAP)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>9.07</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>92.48</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9.07</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5603.79</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Under the terms of the Directors' Stock Accumulation Plan (the &quot;DSAP&quot;), the Reporting Person will be entitled to receive a distribution in The Brink's Company (the &quot;Company&quot;) common stock in respect of all Brink's Units in the Reporting Person's account on a one-for-one basis following the Reporting Person's termination of service as a director.</footnote>
        <footnote id="F2">In accordance with the terms of the DSAP, Brink's Units (each of which is the economic equivalent of one share of the Company's common stock) were credited to the Reporting Person's account as a result of a dividend payment with respect to the Company's common stock. The number of Brink's Units credited to the Reporting Person's account on the Transaction Date is based upon a share price of $92.48 which is the average trading price of the Company's common stock on December 2, 2019, calculated in accordance with the terms of the DSAP.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Lindsay K. Blackwood
Lindsay K. Blackwood, Attorney-In-Fact</signatureName>
        <signatureDate>2019-12-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
