amanda Sorry to hear the responses you've been getting
I don't know about any possible right to referral, however you always have the right to a second opinion (or more! possibly).
If your current doctors are not providing you with the help you need, is it possible to switch to a different GP/surgery? It's not always easy to find a good doctor in this regard, but the NHS website has a review section (granted, more people likely to complain than compliment), and I found a great GP through that, always listened to my thyroid issues, ran comprehensive tests without question when I started showing other symptoms.
My current GP is one I found through word of mouth, having moved away from where the first GP was, and again he is great, listens, treats my symptoms and not just the levels. However, none of the other doctors in the surgery are good in this regard - nice enough, but they look at my results and say, "You're fine, probably stressed". Whereas he goes through my lifestyle, exercise, diet, other conditions, runs other tests and so on and as a result I'm in much better control of my hypothyroidism.
I also find it helps to go armed with your own ideas about your condition - I used to worry that the doctor might think I had been overthinking/over-researching, but that has long gone! I go in, present all of my symptoms, await their response, and if it's something less helpful like, "Well, probably stress/imagining it" I will say, "Actually, could it be [insert problem here]?". I had to do this recently as my regular GP is on leave, the doctor I saw started down the line of, "Are you stressed?" but eventually agreed to check my physical symptoms (because they're physical! Not made up!) and I've since been sent for a number of tests because things are pointing to an actual problem.
I tend to just sit there and say repeatedly, "But I really think I should get x tested" until they agree
