It depends on how much you will be transferring....
Do you have a chequebook on the UK account??
Easiest way, if the amount is not too large, is just to lodge the cheque into your Irish account, day rates in the banks are better than trying to exchange the cash anywhere else and this saves on swift fees.
I doubt you will see significant variations between the banks on rates given.
Although if its V.large the bank will need to do an fx deal in the markets to sell the GBP, so you can negotiate on the rate.
Your best course of action is to ask your Irish bank.
if you feel brave, you could watch the trend in the rates and wait to deposit when GBP is stronger....