I can't comment on the immigration complications to it, but with regards to GRC and access to hormones, it's a right pain in the arse.
If you can afford the private fees, it's simpler. Though you will have to pay £100s for things like blood tests, and medication.
If you would like a broader view of costs, let me know.
I think a lot of people use private services as a stop gap while they wait for the wheels to turn/find a GP who isn't obstructive.