Of course, if you have the money, are anxious to get something sorted out and are sure that the treatment you are getting is the right one then it's your choice.
However, @OwlTwitterings, doctors are trained by the NHS, on taxpayers' money. They are then free to choose to continue working for the NHS or to go private, the amount they choose for both is up to them. Obviously, the fewer hours they work for the NHS, the longer the waiting lists for those whose only option is to use state healthcare (as some time and expertise is diverted to private patients). This has a significant impact on waiting lists for common routine operations e.g. hip and knee replacements. I personally think it's unfair that this resource can be exploited by private care. It is a public good, and only when the public has been adequately served can private care really be considered ethical. if medics had to pay for their entire seven year training themselves it would cost hundreds and thousands of pounds.
The shortage of staff is not helped by the lack of state money invested to train and employ NHS staff, including doctors in sufficient numbers to treat the population, or by a pandemic that has limited non urgent care. Also, when the NHS has to contract out to a private service, like the MRI scans that someone mentioned above, they have to pay for it out of their limited funds, further complicating their budgeting.
Another point - and then I'll get off my soapbox - and full disclosure as my parents both worked all their lives for the NHS as a doctor and a nurse - there has been a huge rise in private, botched ops that have to be rescued by the NHS, especially things like cosmetic and laser eye surgery.
@BigWoollyJumpers you are correct, the NHS is extremely good value for money, one of the best in the world, and so much more cost effective than privatised care systems like the US where it's basically a trade off between insurance companies and big pharma.