Hi!
I had the same problem last september.My problem was bigger than yours.Cause I'm living in Turkey and my reason to renew my CAA medical was to convert my frozen ATPL to CAA ATPL.
Luckily CAA was very helpful to me.
What they say is if you've done your first medical in Gatwick,then you can do your following medicals in one of the CAA approved medical centres.
What you have to do is call them and get the phone numbers of the CAA approved medical centres in your area.
I've done mine in London which cost me 90 Pounds
Good luck in your new job!