Seanieboy,
You'ill need to get an agent in Budapest to sort out your tax liabilities over there!
I don't know if you're purchasing through a company or as an individual. I'll presume you purchased as an individual.
There is a flat tax in Budapest of 25% on your rental income. I don't believe you can make any deductions for expenses etc in Budapest..you pay the 25%!
The good news is that your tax liability in Ireland will be small, if anything at all. YOu can dedect the normal expenses and capital allowances similiar to an Irish property (including the interest on the mortgage used to purchase the property). Due to the double taxation in place with Hungary the tax already paid in Hungary can be deducted from your rental profit in Ireland.