Can you give us some idea of the amount involved, please?
If you're simply trying to move, say, £100 it would almost certainly be cheapest just to transfer the money from one party to the other via Paypal. However if you want to transfer the proceeds of a house sale you'll probably need to use a more formal inter-bank method.
BTW:
You'll upset the residents of Jersey if you write things like "I wouldn't think Jersey would be considered any differently to another place in UK". As they would no doubt tell you, the Channel Islands are proudly independent and most definitely NOT in the UK!