you should be fine, but watch out for the GP they have a nasty habit of striking people off their lists if you haven't been sick for a while, I think its 5 years, but I'm not sure.
To be honest I'm not sure its a requirement to be registered, personally I don't think it should be , as It can be difficult to find one willing to accept new patients, as I found out during covid when I needed to get jabbed in order to be allowed to travel