Hi I ve done it with no problems.
But as Helinut says depends on the school - they (understandably) don't want you spending your money in the US!
If you are going to do it - try the CAA approved school in Florida and you ll have the best of both worlds.
PM and I ll tell you the name of a school resonably local to Sussex who are/were happy to SFH to FAA pilots subject to a checkride.
PW