FYI NHS Counsellors work within same ethical framework as private ones and confidentiality is a big part of that. If the therapist is not clear about who they are sharing information with then you have a right to complain. Probably a bit late for that now but I wouldn't want you to be put off getting help for free if you are offered it!
A good place to find private therapists in your area is
http://www.counselling-directory.org.uk (just check they are registered with a professional body eg BACP/UKCP)
Also remember that it is normal to try out different therapists before you choose one. Shop around and make sure you get the right person this time. As I said, I know several therapists in SW London so if you let me know the area you are in, I might be able to point you towards some good people.
Good luck.