Ulster Bank, yes, also Nationwide UK, Rabo, Santander (if there are Santander branches in Ireland), not sure if they all provide mortgages but Ulster bank does.
You can check with them, with Ulster Bank anyway, to see, if they'd be likely to give you a mortgage.
Though not sure if it's actually going to make things better, if Irish banks raise interest rates, foreign banks in Ireland will likely follow suit.
It might be a better tactic to just fix your interest rate if you wouldn't be able to cope with rising rates. You might also try to save a large rainy day fund, to be able to cope should interest rates rise significantly.