Marie, kitty, I'm sorry I don't think I replied to the original question. I'll try now.
I am also "unexplained" and it is such a horribly difficult and frustrating thing for anyone to have to go through. I'm sorry life has thrown this in your path.
You asked how long til referral. So, here is my history though I know it's all a bit dependent on local policy and can be confusing to navigate - we found it so, anyway.
We pressed the slightly-worried button and saw the GP initially after 8 months and were immediately referred to the gynaecologist (but I was over 35 - younger people generally have to try for 12 months before being referred). Our GP arranged the initial blood tests and DH's sperm analysis while we waited for the gynae appt. Saw the gynae 3 months later, HSG a month or so after that and received our diagnosis of "unexplained subfertility, no reason you won't get pregnant it just might take a bit longer" a little over a year after starting trying.
After another 6 months, so 18 months oftrying in total, we went back to the GP as there was still nothing happening. We knew that due to the postcode lottery the NHS would not fund our treatment (in our area over 35s don't qualify). However, the GP was great and referred us to a different gynae to double check nothing had been missed, as you are entitled to a diagnosis regardless of the local funding rules for treatment. The tests were all repeated, except the HSG, and I also had an AMH test which the gynae arranged but I paid for privately (£40) as NHS policy is only to test FSH as a marker of egg numbers. I never had a transvaginal scan, though, at any point prior to beginning treatment.
The second gynae counselled us that our odds of conceiving naturally were ahead of the odds of an IVF cycle working until around the 2 year point, at which the balance tipped the other way. Based on that, we trusted to nature for a few more months and then signed up for treatment. Because we were treated privately at the same hospital where we had the fertility investigations, we didn't need any more tests or consultations and just embarked on treatment as soon as we were ready to take the plunge. There was no waiting list to start following referral for treatment and I understand it is the same there for NHS funded patients (ie we weren't fast tracked because we were paying). So I started my first cycle 2 years 2 months after starting trying to conceive, and 2 weeks 5 days later had an embryo transferred.
Looking back, the gynae referrals felt an interminable wait and we didn't get that much out of the appointments (not really their fault, as unexplained is unexplained). However, once we took the plunge and said yes to treatment, suddenly we'd started before it felt like we'd even drawn breath.
I should say in fairness that we began IVF somewhat against the consultant's advice which was to attempt the less invasive option of IUI first. However, I didn't feel I had the stamina for too many cycles (of whichever sort) and wanted to use my resources pursuing the option which gave us the best prognosis. I was also conscious, at 38, of time passing. And we were both swayed by the hope that even if unsuccessful, IVF was in a sense the last remaining diagnostic test and might give us the explanation that had eluded everyone so far, to help us make peace with our infertility. (It didn't - still no idea what's wrong but on the positive side, I got pregnant.)
IUI is successful for many people and I think with unexplained infertility there really is no right answer, either to how long to leave it to nature, or which treatment route to take, you just have to follow your instincts and what feels right at the time.