I don’t have any experience with your situation, but I do know that sometimes they use NHS specialists even if you’re paying privately. I know people who have had good and not so good experiences with private elective c-sections, so I don’t think it changes it too much.
I’m having my elective C Section privately later this week (not Kingston, another hospital in London), so can report back. So far going privately has been 100% worth the investment for me, as I was able to choose one of the best obgyn’s in the country for the surgery and for overseeing my pregnancy, who is available on his phone 24/7 in case there are any problems, and it gave me so much peace of mind! That said, I’m quite an anxious person and a wuss so it was probably more beneficial for me than for more level headed ladies 😅
I had an elective section on the NHS and it was a wonderful experience. I think lots of women do have good experiences with them. It’s a lot calmer and just all around better atmosphere. If you’d feel more comfortable paying privately then I’m sure it would be worth it for you after your last experience. But I couldn’t fault my section.