The Nov 1988 one would seem to be correct.
Advice from the Deed Poll Office
If you’re transgender and you want to change your name, you’ll need to change your name by deed poll.
If your change of name is stated on your Gender Recognition Certificate (GRC) or a new birth certificate (for which a GRC is a prerequisite), then this will also prove your change of name, but you’ll generally need to change your name by deed poll first.
If you’re non-binary and you want to change your name, you’ll also need to change your name by deed poll. However, bear in mind that U.K. law only recognises two legal genders (male and female).
deedpolloffice.com/advice/transgender
A deed poll will be enough to change your name in your passport. However, if you want your passport to be in your new gender as well, HM Passport Office will need to see:
your deed poll, showing that you’ve changed your name to one that’s associated with your new gender
medical evidence showing that your change of gender is “likely to be permanent”. This can be a report from a medical practitioner (such as your consultant or GP), or a chartered psychologist practicing in the field of gender dysphoria.