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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-04-30</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000895574</issuerCik>
        <issuerName>Delaware Investments National Municipal Income Fund</issuerName>
        <issuerTradingSymbol>VFL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000740906</rptOwnerCik>
            <rptOwnerName>WELLS FARGO BANK N A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>101 NORTH PHILLIPS AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SIOUX FALLS</rptOwnerCity>
            <rptOwnerState>SD</rptOwnerState>
            <rptOwnerZipCode>57104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Variable Rate MuniFund Term Preferred Shares Series 2021</value>
            </securityTitle>
            <transactionDate>
                <value>2019-04-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </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">The 300 preferred shares reported as disposed of in Table I represent variable rate munifund term preferred shares (the &quot;VMTP Shares&quot;) that were beneficially owned by Wells Fargo Bank, National Association (&quot;WFBNA&quot;). The VMTP Shares were disposed of as a result of a redemption by the Issuer for a redemption price of $100,248.00 per share (which includes a liquidation preference of $100,000.00 per share and accrued dividends of $248.00 per share). Wells Fargo &amp; Company holds an indirect interest in the VMTP Shares listed in Table I by virtue of its indirect ownership of its subsidiary, WFBNA.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>WELLS FARGO BANK, NATIONAL ASSOCIATION, by: /s/ Adam Joseph</signatureName>
        <signatureDate>2019-05-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
