I would pursue the GP line to get a referral.
They will try to put you off with waiting list times.
It must work as i have had my schedule accelerated in the past and received good quality physio at a time that suited me a few years back when i tore the cartilage while trying to lever down a wishbone on a car to do a shock change.
It clicked for a couple of years but the locking was stopped by the physio.
Now i don’t even consider it an issue.
Be like Andy Dufresne, write a letter a day, they can’t ignore you forever.