There is one main group for LGBT doctors and medical students in the UK, GLADD - Gay & Lesbian Association of Doctors and Dentists. They have around 400 members and an active virtual network as well as small regional meetings.
Although it is primarily based around sexual orientation there are a small number of trans members and they are working to be more trans inclusive.
They have a membership fee which is reduced for student members and have a password protected members website as well as regular meetings across the country and an annual new year and summer party.
More information on GLADD can be found at www.gladd.co.uk