Disclaimer: Based on my (sadly) extensive use of the NHS; your mileage may vary.
So my main question is - how do you go about getting your GP to make referrals to specialists?
If you have a medical issue that requires a specialist, bring your medical files from the US. Speak to your GP about your medical history and explain the conditions you have, the treatment you've been getting, and what type of specialist you've been seeing. I've done this and have not had any issues getting a referral to a specialist.
If it's something new, the GP will likely do routine tests first to ensure it's not something basic that can be treated by them. If the tests are not informative, they will likely refer you to the necessary specialist. Or, if your symptoms are severe enough, you can get a referral to a specialist without going through the GP's usual tests first.
I have two other issues that I am concerned about not being able to make my own appointment with a specialist and having to wait for the NHS.
While the NHS does make you wait, I've never found it to be especially troublesome. In my experience, they have a pretty good triage system. It does take some getting used to compared to the US, but I've never personally suffered from having to wait.
If your symptoms are frequent, disabling, not well controlled, etc - you can get an appointment with a specialist in 1-2 weeks. If very very severe, from experience, they will get a specialist to see you in a day.
If your symptoms are troublesome but otherwise controlled with medicine and/or not very severe and there aren't any red flag warning signs of anything being an immediate threat to life - you can get an appointment with a specialist in 3-4 months. (if something changes during that time though, contact your GP or the specialist - you may be able to get your appointment sooner)
Most shockingly to me - how on earth does the NHS not have gynecologists be more active with patients? I just spoke with my friend about this and she said that nurses do the cervical exams and you only see a gynecologist if there is something off. I'm sorry, why is a NURSE performing a medical exam like that?
Personally, I don't have an issue with this. The nurse is taking a sample for testing; s/he's not running the test, not interpreting the test results, and not prescribing medicine or treatment... s/he's just taking a sample that will be sent to a lab somewhere. In my mind, it's the same as someone taking blood from me for a blood-based test. The person taking the blood doen't need to be doctor; the person subsequently directing my care after the results are in though needs to be a doctor.
It may be a US/UK thing. I've found that in the US, nurses are much more restricted in what they can or can't do. Same for pharmacists. In the UK, I've found both nurses and pharmacists are more hands-on with patients and can do more. So long as they have the training and are able to know when something warrants a higher medical opinion, I'm okay with nurses and pharmacists being able to do some initial frontline care.
And what about checking for breast cancer? The NHS already dropped the ball last year when they wouldn't give a pap smear to that poor 19 year old who died of cervical cancer. Are breast and exterior uterine exams done on a regular basis? What about mammograms? There's quite a history of different kinds of cancer - especially female oriented cancer - in my family. My mom's, sister's, and my doctors know this history and check us for it regularly. I feel like I'm going to have to come home to the US and pay a ton of money just to get myself checked from time to time for early intervention.
Sure, there may have been negligence involved if there were signs and/or symptoms to suggest she was more at risk, but that's probably more the doctor's fault than the NHS. And to be fair, cervical cancer in someone under 25 is considered quite rare so if there weren't any warning signs, I can see how it was missed. The NHS does have blanket policies aimed at target groups, but if you have symptoms or a medical history to suggest you may be affected outside the usual demographic, you will get what you need.
I, unfortunately, have rare conditions not expected for my gender, age, overall health, and so on. The NHS literature will advise I don't need this, that, or the other until I'm age whatever... but I've never had any problem getting what I need once I've explained my medical history to my doctors. They've all been understanding that unfortunately, weird and odd stuff happens in medical science, and if there's a good reason to get you a test or procedure the NHS wouldn't normally recommend for your particular demographic, you'll get it. (same for DH with his moles; he gets them checked regularly as he has family history to suggest being vigilant about such things)
I think you'll get quite a bit of resistance if you tell your GP you want this referral or this test without good reason... but if you can explain why you think you need it, I think you'll be fine.
My husband says you have to nag at the GP's for reference to anyone.
This has not been my experience at all; sorry to hear he's been having such a tough time. I've found they won't outright recommend tons of tests for everything or immediately jump to refer to you a specialist, but if you explain yourself, most doctors are willing to listen and take you seriously. You do have to be your own advocate, but I've not felt like I've ever had to nag.
Hope you can get everything sorted; I was terrified of getting care with the NHS before I arrived and since then, the NHS has literally saved my life. I came over thinking I would definitely need private insurance, and never ended up getting it. (I did look into plans though; pre-existing conditions may not be covered so be aware of stuff like this if you do think you want to get private insurance)