I'm trying to get a provisional driving licence - you need a passport or other ID and a deedpoll (possibly also a statutory declaration, it's confusing because of the England/ Scotland laws being different) to explain why the name is different. I think you can put the title that you want on it and the gender marker seems to be a number code and not a F/M so if you can't get your correct gender on it, not many people will notice.
I put M and my new name on my forms, and I'm going to send them my deedpoll, but i haven't completed the process yet, so I can't say that it'll go through.
So, it may be possible to get a new driving licence if you already have one. They're cheaper than new passports and for passports you need a GRC - although those are supposed to be becoming easier to get in the UK, as of yesterday I think!