you will be taxed by UK revenue unless you fill in a form from UK revenue to be exempt from there DIRT, then you have the obligation to declare that revenue to Irish revenue. I have a euro Account with barlcays in the UK, they send you the form when you setup the account, I don;t know if Ulster bank/HSBC are setup/willing to do this for non-resident accounts in the North...
all depends on the size of your deposit, if its sizeable I,m sure they will accommodate you i would guess