I think your right about the variation. I was told it wasnt my GPs decision to ration to 4 a month but the local primary care trust.
For other ailments...Not onlycan you get referred to anywhere you want. Thus dodging the postcode lottery.
You can ask for a second opinion. I was kept waiting for an hour at a local hospital. Annoying as I was first on his list. I felt sorry for the poor buggers later in the day. When he had giving his diagnosis and wanted to book me in for an operation. I said no and asked for another opinion. His face was a picture. Completly flustered he asked where. I told him. And I went see another surgeon at a London hospital. Anotherr wrinkle I discovered. Whilst under the care of one consultant they discovered another minor problem and he referred me to another hosptal. I assumed as it wasnt life threatning I would have to wait ages. But the appointment came through quickly. Apparently a consultant to consultant referrals bypasses the waiting list.
I should have pointed out that kidney thing was pre covid, but still having follow up to find why I am producing so many stones, I had another self referral just before Xmas and the choice was local Nhs or a London private, probably due to Covid restrictions.
Hobsons choice really, unless you are very lazy or have mobility problems, private over Nhs is a no brainer.
There are also 2 types of GP surgery these days, the one I left a few years ago and the one I am at now are completely different. The other I left shortly after it was sold to a large private limited company, my wife requesting an appointment and being told they had none, when she questioned why, no doctors available, they only use locums. It is all about profit, people have died because of the terrible way it is run and I know that first hand.
The one now is old school, very well staffed, never less than 4 reception staff, always answer the phone first time, a long term family business that actually cares for patients.
If yours is poor, check who owns it.