Don't mess with the Revenue, they won't come after you until you are liable not only to tax, but to interest, penalties, surcharges etc...
When did you start renting out your property? If it's before 1 January 2011, you have until 31 October to submit your tax return, if it's sometime during 2011, you have until 31 October next year.
Figure out your Irish taxes ASAP, you might have little or no tax to pay, but you must submit your tax return.
And don't forget about NPPR charge at 200 euro per year, if you moved to the UK before 31 March, you should have paid it by 30 June, thereafter 20 euro fine PER MONTH starts accruing... It's not so bad now, as it's only July, so only 20 euro has accrued but it can eventually run into thousands.