My GP surgery has a policy that they only allow a patient to see a different GP to their registered GP if its
a) An emergency
b) Gynological problem and not an emergency
You can only change GP if you make a formal complaint against your registered GP and the complaint is upheld.
The practice argues that you can change to do a different practice. However the particular GP practice is a very large practice and therer is not much choice in walking distance of my house.