Citizens of any of member state of the EU, resident within the UK, are entitled to be included on the electoral roll. They're entitled to vote in elections for parish councils, district councils and county councils (or, where appropriate, for councils controlling unitary authorities). They can also vote in European parliamentary elections but not in UK parliamentary elections (or in elections for national assemblies within the UK).
Citizens of the Irish Republic, or of any member state of the Commonwealth, who are resident within the UK, are entitled to vote in all elections, including those for the UK parliament and for national assemblies.
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