Basically just go and ask for a referral. I think the the most common grounds for refusal are:
1. They don't bellieve you might have got AS - so take the results of online tests with you so that you can show that you have good grounds for suspecting that you do have it.
2. They don't believe you've got it bad enough to be suffering - so think about this beforehand and be ready to explain how the AS traits have screwed up your life. Social problems with getting friends and partners, and work-related problems are the commonest areas to find that kind of evidence in.
3. They can't afford it. Not much you can do about that at the time, but maybe the NAS or your MP would be interested, as many areas do give referrals for AS, and if one area can afford it, how come another can't?
Try not to say that you've definitely got AS, as that's irrational - if you want a diagnosis, you must have some doubt or there'd be no doubt for the DX to clear up for you. Probably best not to mention disability benefits and job adjustments.
If you're the kind of person who has trouble getting health professionals and authorities to co-operate with you, try to get a friend to go with you. Preferably somebody who knows how to put pressure on them.
Make it quite plain that you want a referral.....otherwise they might pretend that you didn't really ask for one. A good way to start the interview would be to say "I've come to ask you for a referral to diagnose Aspergers' Syndrome." That way they know from the start what you want.
They might ask you how you first came to suspect that you had it. In my case it was my wife who said she thought I may have. The GP suggested that I might be just doing it because my wife had told me to....see how they try to knock holes in your case? I just replied that it wasn't the case and that I was doing it for myself.
They might also ask you why you want to be diagnosed. Self-knowledge is a reasonable answer - obviously if AS is giving you problems in your life, then if you find out that you have it, you'll be better equipped to solve those problems.
Experiences are mixed - some GPs just don't want to know, others are a lot more helpful. Mine made me feel like an idiot but she gave me what I wanted without too much fuss.
I suspect that if you stick to your guns they'll have to give you a referral, as long as your reasons for wanting it make sense. If a patient presents reasonable grounds for wanting a referral and refuses to back down, a GP would be on shaky grounds for blocking it - that could be construed as negligence and it can be reported. But you might still get nothing better than a referral "subject to funds" if money is tight, and then if you didn't get it, I don't know who you could report.
The GP might not say yes or no, but "I'll see what I can do" - if so, it would be wise to ask how long you should wait before contacting them again about it, otherwise you could just be left wondering, and they might be hoping that you'll give up in the meantime.
If the GP says no, tell them that you're not satisfied with that, and ask for their reasons. Write them down and ask the NAS to help you pursue your case.