I'm pretty sure MS still use UPS in the UK for shipping repairs. I'm sure UPS UK also serve the Channel Islands. You can give UPS a call first and ask 08457-877-877. All repairs are done in Europe anyway, either the Czech Republic or Germany.
The UK Xbox Support number is 0800 587 1102. If your console is in warranty the repair is free, otherwise you will have the pay. If you have to pay, the cost covers both the repair and the shipping costs.