well first of all you need one who has an interest in menopause (because not all gynaes do...some specialise more in surgery, endo, that kind of thing...)
Word of mouth is a good way- recommendation but I don't think it's a good idea to put names on forums because there is a risk of people discussing the consultant (positively and negatively) which can get into libel territory if it turns nasty.
It's best to look at the private hospitals or women's health centres (if any) in your area, look under the headings of Consultants, and see who they have or do a google search putting in search terms ' eg menopause gynaecologists Exeter, Bristol, Taunton, wherever you happen to be. Most consultants have their own websites now.