as far as i am aware there is nothing stopping banks issuing their direct debits on any bank within the SEPA zone (even outside Eurozone) so long as the bank is linked to the Sepa system.
So technically you can pay your mortgage from a UK GBP account. All transactions travel in EURO (regardless of where they originate from).
the only issue you will have on the account side is that banks (generally) require you to be resident in the country they operate in. However, from what I hear, this will be relaxed in the near future to be resident within the SEPA zone. This will (truly) open up Europe as one banking market.
Irish banks are shagged then