Iain Dale's made a bit of a booboo with his The Irish Should Not Be Able to Vote in UK General Elections - as he acknowledges, UK Nationals do have the right to vote in the Dail elections, though not in referenda or Presidential elections. My father, a UK National, tells the story that the day the referendum was held coincided with a European election, and he turned up to vote in that election. He was given a ballot paper for the referendum, and when he pointed out he was British, the teller said "ah sure, then you'll definitely want to vote". I also remember one local politican calling to the house during the 1982 elections and saying "ah, they've never actually fined the Brits for voting" (for some reason my parents were still getting polling cards for the Dail elections).
There is another point that needs to made that may be relevant to Iain's posting. Before 1984, the anamoly was that UK nationals couldn't vote in Ireland, but Irish nationals could vote in Britain. At that point, many Irish citizens were probably able to claim UK nationality anyway, but Mrs Thatcher felt it was unfair. It is suggested that she told the Taoiseach (presumably Garret Fitzgerald) that she felt the anamoly should be corrected, and it was up to Garret which way it went (ie, the Irish could either give the UK nationals vote, or she'd revoke their rights).
Recognising a courageous decision when he saw one, Garret took the safe option.