It's difficult to cost a private op unless they offer a 'package'
You will have to pay for the bed/room
You will have to pay the Surgeon or Gyne
You will have to pay theatre time - and this can be variable. EG when I worked in a private hospital if we were out of normal hours we were paid £35 call out for each patient and if a cse went over 2 hours we got an extra £35 per hour
You will have to pay for an anesthetist, the nurses and ODP are usually in the thetre price.
YOu need to pay for any drugs prescribed. This one you can cut down by asking your GP to prescribe painkillers before the OP so you go in with your own drugs.
Then you have to pay for any equipment used, not big equipment but the disposable stuff they use and this can vary a lot. If somoething drops on the floor it can't be used, but the cost is added on to your bill.
Unfortunately you don't have much barganing power, the insurance companies have. The hospital I worked at sent the full bill to either self funding patients or their insurance company.
Self funding patients all had to pay the full bill.
The insurance companies would often pay 80-90%, but because a private hospital cannot live without the insurance companies they just swallowed the cost (passed it on in other ways).
I know it is a waste if you have insurance but would you consider the NHS? Even just for a referal, so your GP can state it is not fertility treatment.
Then go back to the insurer's with that.
One thing to be aware of, and people don't normally think of this is that if there is a complication that means you have to be transferred to an NHS hospital you will have to pay for the NHS treatment.
Even if there is a complication and you are transferred to a ward for a day or two that will eat up money quickly.
Check what facilities the hospital has, some have ICU and HDU beds, others don't.