It may depend on area to a certain extent, but when I tried through the NHS to get a diagnosis, whilst my GP was happy to refer, that's about as good as it got.
It took nearly a year to get my referral, I talked for about an hour to a psychiatric nurse, I never saw a psychiatrist. I had brought along about 20 pages of evidence I'd written of how I matched the DSM criteria, and although they took it from me, I can't say that they read it and given how quickly they got back to me (that afternoon) I don't think they ever did.
The upshot was that after this discussion, I was told that because I was functional (i.e. I had a job, a marriage and a home) I could not possibly have it. Never mind that those things were suffering badly as a result of not being diagnosed and that was why I was there.
I was told to take up yoga.
Between that appointment, and having big issues at work directly related to failings associated with ADD, and feeling I was never going to be anything other than useless, I ended up on anti-depressants for the first time in my life when what I really needed were stimulants.
Fast forward a year or so and I am seeing a private doctor in London. He hasn't formally diagnosed me yet, but based on all I said and my utter frustration over my wasted potential, was happy to give me a prescription for Elvanse (Vyvanse in the US) to see how it went. It has genuinely has turned everything around for me. It was never an anti-depressant I needed, that was just a sticking plaster that never addressed the cause of the problem to begin with. And now I am currently struggling with the withdrawals from Venlafaxine, which is one of the worst to get off from, but I no longer need it and the side-effects were just making things worse.
If you can afford it, I really would suggest going private. Not just because it's quicker, but because the NHS for the most part seemingly does not have the resources to be interested in adult ADHD except in dire situations. They'd rather pay to mop up the result of a missed diagnosis and unfulfilled potential with anti-depressants which seems counter-intuitive to me, but hey.. it's policy.
Good luck!