Hi -
Our DS played alto sax, took grades up to Grade 8 and got distinction, and played in school jazz band, annual school stage musical, and later the County jazz band. Also did 'A' level music at school.
I assume you mean Associated Board exams - there is also Guildhall (or is it called Trinity now, I always forget - was Guildhall Trinity at one time.) AB is under £50 for Grade 3, prices increase as Grades go higher, as obviously more needs to be tested and to a higher standard. Even though it is a 'practical' test, that is Playing, there is also some theory, scales, sight reading etc involved. It's twenty years since our DS was doing it, so I'm out of touch but here is the AB scale of fees, and you can get more details on their site:
gb.abrsm.org/en/exam-booking/exam-fees/
I agree not to 'push', but on the other hand it won't be that many years before he is into GCSEs etc, and it's not much good saying don't want to do it in case it's hard and might fail. So having a bit of pressure and having to work towards something is probably a good experience to get used to. Especially when it doesn't matter THAT much how high he scores in music, unlike GCSE, which is a bit more important.
As a TA I taught informal recorder lessons in primary school for ten years, and I think the more musical experience a young person can get, the better. Besides the music, it can be a valuable social experience.