I can recommend Prof Nicolaides - I had laser ablation surgery carried out by him a couple of weeks ago at Kings for twin to twin transfusion syndrome - NHS, he was fantastic. If you are in the greater London area your local hospital should be able to recommend you to the fetal medicine centre there. I am not sure if he personally carries out all the cvs.
Just read the rest of the thread - he does do all the CVS himself (or he did in 2009 when he did mine). Another obstetrician will do scan/bloods and prepare you and then he bursts into the room like a caped crusader, carries out the procedure and crashes out again. He was with us for no more than a couple of minutes!