Swapping schools is theoretically quite easy. It happens all the time, although usually after some of the exams have been attempted and usually between distance learning providers.
If you have done a complete distance learning phase for a subject your new groundschool might be comfortable to accept that at face value and sign you off for the exams after you attend a short classroom phase with them. If they are, ask your old groundschool to transfer your training records to the new groundschool. You should probably also inform the CAA as a courtesy
[email protected].
If it is less cut and dried and particularly if you are going full time and therefore entering a more tightly structured training environment they are likely to ask you to start the course again from the beginning. If that's the case its not neccessary to tell the CAA and there is no point transferring training records (although your new FTO might like them as background information).