Not sure but you would probably need to shop around even more widely than three banks. If they are charging a transaction fee in addition to the forex margin and you don't qualify to have this waived then haggle or get somebody who does qualify to have this charge waived to convert the money for you (e.g. some or all OAPs used to get this perk - not sure what the story is these days).
Alternatively if you have a credit card you will probably get a better deal by sticking the money on the card and then withdrawing it abroad.