Have you tried halifax, since they are mainly uk based. I think you should be able to go into one of their branches in ireland and set up a uk bank account. They would be able to send/fax over all the documents that you sign here in Ireland.
If you cant do that then you could go up to the north and open an acount yourself, That way you can manage the account on line. If you needed to lodge money into the account you can do it in a halifax in ireland but it would take a couple of days to go through.