Choosing hospital/consultant for 2nd ovary and fallopian tube surgical removal

[MPP]

Looking for some pretty serious advice please regarding choosing a good private gynae oncologist and hospital in London.
I had an ovary and Fallopian tube removed 13 days ago, my 1st major surgery (all I had done before was small umbilical hernia).
I wasn’t happy with hospital service and overall communication with consultant/ surgeon. I found them through my health insurance authorised lost, so had no reference point or recommendation.
Consultant today said she found out during surgery that other ovary is not looking good, and would advise me to have it removed too.
fortunately I have a health insurance (not a great one but good start!) which allows me to have a second opinion,
my query is:
>> What’s best way to go about finding a credible & experienced private gynae oncologist and good quality private hospital for 2nd opinion and possibly 2nd surgery?
thank you so much!

The Royal Marsden is the centre of excellence though I have found them really slow and not great with communication, I wonder whether everywhere is stretched. HCA were the other group I had recommended. I found it difficult to choose an individual consultant, I liked at edit was involved with the gynae charities, but that didn't help much so I just had a referral to the hospital and they allocated me someone appropriate. Is there a FB group you can ask on?

Oh and I think both provide a "second opinion" service. My hospital originally said they'd refer but then in the end I had to do it through my GP.