As far as I am aware you can change GPs mid way though a MH plan provided you are attending the same psychologist or other MH professional (the one you were referred to by your original GP) or they can provide a report.
You may find the following post helpful (a couple of years old but I believe still accurate).
(Links are not live, please paste as one long line into your browser)
In addition have a look at point 1.4 entitled:
"Should these services be provided by the patient’s ‘usual doctor’?"
In the Government's Health web site:
This too seems to confirm a change is possible.
If still in doubt ring up the surgery you wish to attend and confirm
Hope this helps