It's now way easier for USian transgender people to get their passport corrected. The new rules are published. From now, people need only be receiving an appropriate course of treatment and do not need surgery. This is established by a doctor's letter. And the ever-helpful National Center for Transgender Equality has a sample letter available. Only certain types of doctors can write the letter. They haven't yet stated what they will want from foreign doctors, but I'm going to call on Monday to ask. I imagine that in the UK, it should be fairly straightforward.
Why this is good news
There are a bunch of obvious reasons why this rule change is good. People can have an identity document that matches their presentation, thus making border crossings a lot easier. People in the US who do not have the thousands of dollars it takes for surgery can now get a passport. People who, for health reasons, cannot have surgery can get a correct passport. Trans people will no longer be subject to mandatory sterilisation in order to qualify for a correct passport.
FTMs could sometimes get away with just having top surgery to meet vaguely worded rules, but after Thomas Beattie (the pregnant man), some officials were more aware that some FTMs had male ID but were still fertile, and sought to stamp that out. Also, MTF surgery is widely understood to include sterilisation.
There are a lot of trans people who do not want to stay fertile, and they shouldn't have to. But there's a reason that phrases like "mandated sterilisation" make one shift uncomfortably. It's a human rights violation. Trans people should have the same rights to become parents that cis people have. Cis people are not forced legally to decide whether they can have appropriate identity documents or can produce offspring. Now, at least for passports, trans people are no longer forced to make that choice either.