Through my work i get access to Bupa and in Edinburgh they have the 2 Spire hospitals that are their own with their own staff. The doctors / consultants do split their time between NHS and private.
I can only speak to our circumstances and when we were trying to conceive my wife was told by her NHS doctor that she could have a 'tumor' and that she could join the waiting list to be seen. We made the decision to go private right away and had a diagnosis and treatment, and had conceived all before the first NHS letter came in to say come for a chat. Took about 6 months. Imagine leaving someone for 6 months thinking they had a serious issue like a brain tumor. I am just thankful i could afford it.
The NHS needs to get back to its roots, being a service for people who are genuinely ill, not some influencer who has a wonky nose and feels depressed about it. for the amount of money it gets there has to be some amount of wastage.