or does a FII need to sign all the hours he has flown with a trainee FI. The CAA is checking the logbook to issue a FI rating, do they need to see every flight made to obtain a FI countersign by the FI instructor?
For any course of training, the school should put a nice stamp in the log book and certify the training. Failing that, either the instructor or someone responsible at the school would sign the paperwork that goes to the CAA. So either way, for a course of training the CAA should have some evidence that the hours are correct.
Once you have a licence and are flying alone, you can log what you want and no one will certify it. For a course of training for the issue of a licence or rating, each flight would not need to be signed individually, it would all be signed off at the end.