http://www.electoralcommission.org.uk/faq/voting-and-registr...
"To vote in a UK general election a person must be registered to vote and also [...] be a British citizen, a qualifying Commonwealth citizen or a citizen of the Republic of Ireland"
http://www.dublincity.ie/yourcouncil/votingandelections/Page...
"Elections for Dáil Éireann: Both Irish and British citizens can vote in elections for Dáil Éireann (the lower house of parliament)."