I can't say how easy it would be for you, because it depends entirely on your own case and circumstances and the attitude of your GP and surgery toward your situation. I know it's possible in the right circumstances because I'm on bridging treatment right now, but it wasn't entirely straightforward. What I think helped is that I was very firm and consistent in pressing for it but without being pushy or demanding, and also that I demonstrated (in their eyes) a strong certainty and commitment to transition from the outset (they are very wary of moving forward with HRT when they think the patient may be uncertain or has other confounding issues to deal with).
Early last summer, I wrote to my GP saying that I had gone full time and would be contacting her soon to request a letter (for my passport change, etc.) and to ask for bridging treatment. I wrote to her again 2-3 weeks later, once I had changed my name legally, and made those requests. At that time I also drafted a lengthy statement of informed consent detailing that I was of sound mind (I'm sure that's debatable, but let's skip over that :p), understood the risks and limitations, and consented to starting treatment. At that point I hadn't had my psych evaluation, so she said to come back after it and we would discuss treatment. The psychiatrist said I was as clear cut a case as she had seen and that HRT was the next logical step for me. I returned to my GP to discover that the practice managers had held a meeting where they'd decided that they weren't comfortable with it and wanted to leave it to the GIC. At that point I was in a horrible place mentally. My SO wrote to them explaining how badly my dysphoria was affecting my daily life and asking them to reconsider, given that my GIC appointment was still 10 months away. After another practice meeting, my GP contacted one of the specialists at the GIC who said that they ought to consider treating me. I had to attend a second psych appointment a few weeks later (that's normal but it should've been scheduled with the first one, only the admin staff hadn't booked it), after which my GP finally agreed to prescribe me HRT.
The whole process took about four months. Given that I'm unlikely to get my GIC appointment before June 2015 and probably won't get a follow-up appointment where they might have prescribed hormones until September or so, it's been a lifesaver for me. I've now been on HRT since October.
One thing I would say is don't threaten them. IMO, that is likely both to antagonise them unnecessarily and flag you as having mental health issues that need to be worked through before they're willing to offer endocrine treatment. Do be prepared to be knocked back, and be ready to keep trying. In the right circumstances, you may be able to convince them and turn an initial no into a yes. Otherwise, as Leila says, you could try another doctor, or another surgery. That was going to be my next avenue if I hadn't been successful with my current GP.
And good luck.
I know how you must be feeling right now and it sucks, but hang in there. It will all be worth it when you get the treatment you need.
