I've heard about this law, from the couple I just mentioned who relocated to London.
The UK once was one of the few European nations that did not recognize the new sex of a transgender person. That has changed with the Gender Recognition Act of 2004.
I've checked the details just now, after reading a few articles on the Guardian. It looks like two years of medical supervision while living in the new gender is all that's required to be legally recognized as the new gender, for all purposes including marriage and titles. Surgery is not a requirement, which is great for my couple who are non-operative; they would've been forever considered men under US laws.
The surgery, to be honest, is a very expensive procedure with many risks, and should only be undertaken for body image issues. I don't like the idea of being forced to take the surgery route just to have that magic letter "F" on my passport. To that end, I think this law is a very good move, and more nations need to consider adopting similar measures.
Back home, here in California, I can get a driver's license with the corrected gender marker upon presenting a doctor's report, and it's good for identification and employment purposes. However, it doesn't change my LEGAL gender, which will require surgery, and is a must for marriage purposes, and for changing federal paperwork such as passport.
Gender Recognition Act