While it's true to say that the hours in your log-book will still count, it's also the case that the CFI of the training facility which completes your training will need to certify to the CAA when he endorses your licence application that the training syllabus has been completed in full. It's unlikely that your logbook contains sufficient detail for him to do so, I'd certainly need to see more evidence than a couple of words in the remarks column! Note, I'm not suggesting that you have falsified you logbook; simply that more detail will be required than is usually included in the remarks!
I'd advise that you get in touch with the school, get a photocopy of all your flying records and have the CFI sign to certify that they are accurate. You can then show this to the CFI at your new school and he will probably keep a copy with your new record there. If a student leaves my school for any reason I automatically give him copies of all our records on his training to take with him to a new school.
Good luck with your flying!
3 Point