The Fetal Medicine Centre is the private arm of the Fetal Medicine Foundation, a charity set up by Prof Nicolaides for research into fetal abnormality detection and treatment. The FMC on Harley St exists to fund the work of the FMF.
What you get on the NHS is a bit of a lottery depending on where you live, how old you are and what your perceived risk is (for eg, some places in the UK will only offer you a nuchal scan if you are over 35 or 37. Other places will offer you a nuchal whatever, some routinely suggest to older mothers (37+ in many places) that they consider invasive testing etc etc).
If you are not getting what you want to have on the NHS, then the FMC is an option if you can afford it and want to have a particular test. I am pants at links but will try. This is the website www.fetalmedicine.com , complete with details of the testing they can do and the price list.
All scans are done by obstretricians trained by Prof Nicolaides who work part time at the FMC and part time at Kings (the Harris Birthright trust, to which you can get NHS referrals, although I don't know how). The invasive procedures are done by the Prof himself. I would definitely recommend it as it gave me huge peace of mind being an older bird but a lot would depend on what you were hoping to find out from the scans, tests etc and what you would do if you didn't hear the news you were hoping for.
Hope this helps. X