Cross dressing is not illegal no. Doesn't necessarily mean you can do it at work though. If there is a uniform then you would have to wear it, right? Maybe you would be able to dress female but it would depend on your employer and their opinion with this kind of stuff, especially in a public facing position where I expect a lot of employers would want you to be able to pass well. It all depends though, I am pretty sure that we are protected by anti-discriminatory laws but that does not mean that if they don't like you they can't find another reason to get rid of you, you know? That is the same with anything and anyone though, in any job, if you have a bad boss. Like my sister got a zero hours contract in the spring for a job but because they took a dislike to her she has gotten zero work.
I guess the most important thing would be how well you pass. If you can easily appear and sound female I doubt many people would care much so long as you can do the job. I am no specialist on employment and rules though. So take a grain of salt please!
Oh and don't be scared of doctors. If you are serious about this you really should go and tell your GP and see what he can do to help you. It is their job!
NP for the info.I don't mind helping at all.