As someone originally from Northern Ireland but who works in Scotland and England, I am fairly militant about this. I normally just threaten to walk out of the said shop/establishment if they refuse accept payment with a N Ireland (or less frequently, Scottish) banknote, in 7.5 years of doing this I've only actually had to leave once, in all the other circumstances the cashier has relented.

If you're less brave than I am, try the Self Service checkouts in any major supermarket which generally accept all Sterling banknotes without question. Alternatively, the nearest post office will exchange Scottish/NI banknotes.