Good luck on your first consultation! I can't tell you precisely what to expect, but I can tell you what my first appointment with my GP was like.
I requested to see a male doctor, and that was all fine. The moment I went in there, I told him my situation: I identify as FtM and I want to start on T as soon as possible. He asked me a few questions such as 'how does being identified as female make you feel?' - "Disgusting. Disgusted," was my answers. He asked a bit about my personal life such as do I have a job and/or a significant other/partner (so you might be asked these). I live in Norwich so there really aren't that many resources for the trans* community, but he did say he would refer me to a nurse on the mental health team in the same clinic - who I've been to - and really, that was it.
Some of the questions your GP will ask you might feel as if they're intentionally trying to trip you up, and it was frustrating for me when he asked for further explanation and detail on being identified as female and not wanting to live with it. But just persevere, keep as much of a level-head as you can, and remember that no matter how little it seems might've been done in the consultation, it is the first step! And each step will keep getting you closer and closer to your goal!
I hope this helps a little bit, or even provides a little bit of moral comfort. Good luck!