You didn't say which rating you are training for however; your exam passes should be entered onto the
licence application form immediately after you have taken them and it should be signed by the examiner. This is your proof that you have passed an exam. If you failed an exam you should be given a copy of Form 252, notifying you of your right of appeal. The CAA also have copy of the F252 to ensure you don't take the same exam twice.
Usually the school will keep the applicatioin form on your training record folder. In some cases examiners fail to complete the paperwork when they should. The next time you go to the school ask to see the completred form; if it is not there or completed insist that it is.