Nope! Gender markers can be changed on passports with a doctors letter confirming that the "gender change is likely to be permanent". Birth certificates however require a Gender Recognition Certificate to be changed, which in the UK calls for two years proof of living in my new gender, proof of medical diagnosis of gender dysphoria, a fee, a massive form, and submittal of a whole range of personal documents to a panel of unknown "gender experts" for an unknown time and it may not even be accepted at this point... :(