Or did you mean paid in sterling and mortgage in euro? if so, maybe you will have to create a sterling account in the euro area or a euro account in the UK and have the funds transferred each month. You may need an overdraft facility to meet the funds if the date do not match, but I'd say could negoitate the FX cost with your manager.
I'm sure being a customer of the bank (which ever applies) you could say,
"Look I earn £3000 pm that comes into this account. I will take my business elsewhere if you do not quote me a competitive FX rate. I do not want to pay the retail rate you offer the ordinary Joe Soaps that walk in here but somewhat better."
Our experience of this scenario was that banks in the south were happy to make allowances for transfer of funds at preferential rates, but the bank in the north that salary was being paid into wanted exorbitant charges to wire money. We take cash out in north and lodge each month in the south. It's a pain but the cheapest way to do it for the moment. Any suggestions from others would be welcome too.