There should be no problem having current account and mortgage in the one bank - don't see why there would be. It can also be of help to build up a relationship with one bank, so long as they know that you also shop around and aren't staying with them purely through inertia.
BoI also offer free banking, but I think you have to have a credit balance. Before going to the hassle of changing banks (and it is a bit of a hassle, though equally can be well worth doing), check whether you qualify for free banking (i.e. whether you're regularly using overdraft facilities or not, and whether you use online / phone banking), and if you do, then register for it immediately. If you don't qualify on the basis of overdraft, check overdraft interest rates on current account offers, as these may ultimately determine how hard you're hit for charges.
My other half banks with Ulster Bank and has found it sometimes very frustrating - they closed the account down once when they shut a branch, and transferred the balance to another account *without letting OH know*! - and messed around with a savings account as well.
I bank with BoI and have found them reasonably good, and both quite flexible and remarkably cheap when I've needed bridging or guaranteed draw facilities.