Hiya all
Having gone through this process recently, it's not particularly challenging. The online documentation is a bit vague, and I had the "customer service" people at HM Passport Office helpline interpret it really badly. A Gender Recognition Certificate is acceptable, as is a letter stating that you have changed gender and that it is likely to be permanent.
Any other documentation showing that you're under treatment, or have had surgery of some kind is useful, but not vital.
Just one thing: this letter must come from a doctor or a registered medical specialist. Psychologists are not considered an appropriate authority.
The fast-track service will get you a new passport in 10 days.
Good luck
Julia