I am currently doing the same thing changing my provider
It seems that it can be long winded, but the provider i am going to has done a lot of legwork on my behalf so all credit to them, For me its a few e-mails and hopefully that is it.
My old training provider is reluctant to pass records on though. So i think the course of action is to inform the CAA of your request to change providers, then have them request your records or the head of training at your new provider can request them and hopefully your old provider will realease them.
Good luck
