Hi !
The JAA ATPL conversion depends on your previous experience level!
IF: Have an ICAO issued ATP and over 500-1500 hrs multi crew, multi engine experience, than you MIGHT be exempted from the course itself, but most likely will have to sit the exams, although all 14 of them, and then a skill test on the same type you have a rating on. ( So you have to find a sim, an examiner etc. for the skill test, most schools do not help you out with that...)
IF: ICAO ATP and over 1500 hrs, no need to sit the course, just do the exams, but the number is at the discretion of the training facility. (they've told me still all 14 exams....4000TT, 3300 B737)
AND IF: you are very experienced ( I think 6000TT with 500 PIC on Multi crew, multi engine, bla-bla), then you only need two or three exams to be done...
BUT! It seems to me that every case is different, you might want to get in touch with either the UK CAA, or an approved Ground school provider, to help you with your case, and to see what amount of exams/courses they want you to sit.
The above mentioned schools are all good, drop them an e-mail, and see what turns out of it !
If you're stuck send me a PM, I'll try to help out !
Good luck !
CJ