"The Gender Recognition Act 2004 (GRA) was an Act of the Parliament of the United Kingdom. The Act allowed trans people to acquire a new birth certificate reflecting their acquired gender."
The GRA is the law that allows trans people to change their legal gender without undergoing surgery. It is not compulsory to have surgery in order to change your legal gender, but it has been reported that some hospitals and doctors are refusing to change your legal gender without it.
According to British Law, you can legally change your sex without surgery as long as you have a diagnosis of "gender dysphoria" and fulfil other requirements.