Many large hospital trusts have websites listing their staff and their specialities. Try your local large NHS hospital website, find the specialist you need and then, if you want to go privately, see if they take private patients. Lots of NHS hospitals do, although with the 18 week referral to treatment target, the waiting time in the NHS is not like it used to be. At least if the Dr is employed in the NHS there is some guarantee that they are qualified.
Hope this helps
mel