Having a good reference will help tremendously, particularly if it's in the right name. So I'd suggest coming out to your branch's Personnel Dept.
Have you told that supervisor's boss what they're saying to you? What about one of those managers who have complimented you on your work? See, you're probably worried about being seen as whiny if you complain... but the law gives LGBT people special protection from harassment. The thing is: you have to tell them you're trans before you can get that protection.
The 'atmosphere' and 'comments' you mention are unlawful, and your colleagues would be disciplined or even fired if they try that with you. That's because the Equality Act 2010 places a duty on your employer to protect you from such harassment. There's plenty of info about the Equality Act on the Web, but this is a good place to start:
http://www.pfc.org.uk/Equality.htmlHave a good read about your rights, then get in touch with whoever is responsible for Personnel/Human Resources at your branch. Tell them you're trans and plan to transition on the job, and make them aware that you're worried about potential harassment from your colleagues - particularly that supervisor. Make notes about what they've said, when they said it and whether there were any witnesses. It doesn't matter that they're higher up than you are: they will be disciplined if they're breaking the law. If it helps, take a printout of the relevant bits of the Act as a reminder of your rights and use it to show where that supervisor is breaking the law.
Any time anyone is judgemental or makes you feel awkward about this, make a note and tell Personnel about it. It isn't your job to make your colleagues behave; it's theirs. But they can only do it when you come out to them.
Did you know that your employer has an LGBT staff network? Many large companies have similar organisations. You might want to get in touch with them to ask their advice, because many of them will have come out at work & will know what to expect. I'll PM you the link.

I'm a manager and I've recently completed a course on this very subject. If you'd like some advice on specific incidents, feel free to PM me.