Generally speaking, when you change pounds at a bank store, they will already know you and you will only have to identify yourself as a client of your entity.
If you change pounds at a holiday money provider´s office, on the street or at the airport, you will need to provide a valid and current identity card (passport or resident´s identity card called DNI or NIE in Spain). Have in mind that the driver's license is not accepted as a valid identification document when changing Euros to pounds.