If you check this link out, it lists all the schools that are created to provide FI training by the CAA.
CAA Site Thingy
On a personal note, I would also recommend Stapleford for the FIC. Keith is a very experienced instructor and spent 25 hours with him learning how to fly properly. Glad to hear that Tony has been made up to FI Instructor. Another top lad but don't ask him to do any aerobatics though......
Most school will prefer their own brand trained instructor, but that is by no means a barrier to finding employment after training has completed. Pick a school that you think is going to provide the best training for yourself and worry about getting a job afterwards.
Oh, and good luck.