The costs tend to really vary. I don't have private health insurance but I have had to rely on going private several times due to the indifference shown by my GP so I can give you some rough estimates.
I live in London so have found that initial consultation costs between £150 and £250 - anyone on Harley Street I have never found to charge less than £250. I had to see a gynaecologist privately just so he could write a letter to my GP insisting he refer me to his clinic on the NHS, a year and a half later I findally had the diagnostic laparoscopy.
I went to A&E with severe abdominal pain this past July, they didn't care to do an ultrasound scan - I had to wait 2 months for my GP's referral to come through and they found a large cyst basically crushing my uterus and bladder... My specialist consultation appointment at a BSGE clinic has a three month waiting list so I decided to pay to have an MRI privately as it's important to have this before surgery is carried out. I figured a 3 month wait for the appointment, God knows how long I'd have to wait past that for the MRI. My MRI is costing around £800. Thankfully I have a very supportive family otherwise I wouldn't be able to afford this.
To have surgery privately can cost anywhere between £5000 and £15000 - depends how serious the endo is and how many organs it is affecting. There was a renowned gynaecologist who specialised in radical excision technique, he recently retired, and I believe for most serious cases the cost was around £20,000 - so as you can imagine it can be a serious financial strain.
It's really sad that we have this wonderful (in principle) health service yet you just get sicker and sicker waiting there just to be seen. I would advise, as some others have done, if you can afford it just get an initial appointment or two with a private gynaecologist to speed things along.
If you want advice on what to ask them for I'll try my best to help.