Private treatment in the UK?

Apologies in advance for a long post. I've had fibroids for a while but the bleeding/pain was mostly manageable until I had a PE earlier this year and was put on blood thinners. The fibroid+ thinners combo has made my periods a living hell. Extremely heavy bleeding and clotting. I've had to have blood + iron transfusions twice because of it. As a result I was referred to a gynaecology consultant but because of the NHS backlog my appointment took months.

I saw the consultant last week who confirmed I have two big fibroids and numerous small ones. He said because of the waiting list I wouldn't be able to get an open myomectomy before the summer, but he wanted to put a camera up there to see if he could remove the smaller ones in a day procedure. I asked when I would be likely to get an appointment for that procedure and he said it would be quicker than the open myomectomy, and they'd be able to get me in 'soon.'

It felt like there was a bit of hope on the horizon, then I got an appointment letter for the 25th November 2025. This isn't for the actual procedure to remove my big fibroids or the small one, just to put the camera up there and see. That's close to a year of living like this. I expressed to my consultant how this was basically impacting every area of my life and destroying my quality of life. I know he can't help the waiting list but I'm not exaggerating when I say I cannot live like this for another year. So I'll have to find a way to pay for private care.

Has anyone ever undergone private treatment in the UK (London). Would be grateful for any recommendations/experiences.