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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-09-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001253706</rptOwnerCik>
            <rptOwnerName>HENRY DANIEL R</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>Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-09-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1.27</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>73.39</value>
                    <footnoteId id="F3"/>
                </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>1.27</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>622.88</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Units (each of which is the economic equivalent of one share of The Brink's Company (&quot;BCO&quot;) common stock) credited to the Reporting Person's equity account under the Plan for Deferral of Directors' Fees (the &quot;Plan&quot;) will settle in BCO common stock on a one-for-one basis and shall be distributed in accordance with the Reporting Person's deferral election either (1) following the Reporting Person's termination of service from the Board of Directors or (2) on a future date selected by the Reporting Person at the time of his or her deferral election.</footnote>
        <footnote id="F2">In accordance with the terms of the Plan, Units (each of which is the economic equivalent of one share of BCO common stock) were credited
to the Reporting Person's account as a result of a dividend payment with respect to BCO common stock.</footnote>
        <footnote id="F3">The number of Units credited to the Reporting Person's account on the Transaction Date is based upon a share price of $73.39, which is the closing price of BCO common stock on September 3, 2019, calculated in accordance with the terms of the Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Lindsay K. Blackwood
Lindsay K. Blackwood, Attorney-In-Fact</signatureName>
        <signatureDate>2019-09-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
