There is quite a bit of misreporting over the situation with "X"/Unspecified markers on Australian passports that has recently been announced. To clear up the situation, there's a very good post here, on Global Comment. The short version is that there are two options:
Transgender people can now get a gender-appropriate ("M"/"F") marker without having gone through surgery, as was previously the case. Hormones still seem to be required which still isn't perfect but it's very good news for Australians and removes "genital essentialism" - the erroneous link between genitals and gender.
Intersex folk can get an "X"/Unspecified marker with a doctors letter. (I've not seen any confirmation that this is truely optional and might not be forced on people - an "X" marker coudl get you in a lot of trouble in some countries)
And to clear up the confusion:
Transgender folk CAN NOT get an "X" marker. You must be Intersex to get that. (And no, going all Harry-Benjamin-Syndrome on your GP and claiming that being Trans is an Intersex issue isn't likely to work here)
As for the UK situation, there are no current plans to introduce an "X" marker for anyone, and no "X" passports have ever been issued. Apparently there have been previous discussions with the Trans community and the community "didn't see a need for it", but that appears to have been some time ago and likely before the non-gender-binary community was quite so prominent in terms of campaigning.
What we've pushed for recently is for government organisations in general to have to justify use of storing and using gender at all as part of their Equality Impact Assessments. It has come up in discussion with the Government Equalities Office and may be in the Trans Action Plan when they publish it. This isn't just a transgender issue but can also be a wider feminism issue, if you look at the position of organisations like the DVLA who can't see why printing "Mrs" or "Miss" on a driving licence is an issue, when they don't print titles for blokes at all by default. ("Ms" is available only as a write-in option)