My experience is that private health insurance will pay out for initial diagnosis (in my case they paid for an MRI and DATscan to confirm diagnosis) but they will not cover any ongoing treatment.
I also had a personal Critical Illness Cover policy, to cover some of my mortgage, that paid out.
However, to my knowledge, once you’re diagnosed it won’t be possible to take out new cover.
My experience with the NHS has been very positive, though it can take time to get appointments.
Hope this helps.