@SnorkeMor - "IME the only private clinics offering assessments that lead to support are ones where clinicians also work through the NHS, as otherwise the diagnosis lacks credibility and support cannot be accessed."
That's not actually true - the NHS will recognise any diagnosis performed according to standard practices (with the accompanying full diagnostic report). It's based on evidence, methodology and conclusion rather than the person who performed it. At least, that's my experience and that of the (many) autistic folk I've spoken to.
I'm certainly grateful for private clinics - I would never have done mine through the NHS (even if my GP hadn't been an a-hole about it and refused to even consider it), because I'd rather a child could take that rare slot and be given the support and opportunities I never had a chance at.
"People can self identify as much as they like, this doesn’t translate to anything useful at all for them."
I disagree - it really can. It often goes hand-in-hand with spending a lot of time talking to other autistic people online - not in a "watching TikTok videos" way, but rather in a "can we talk about this like adults?" way - and gathering both evidence for/against and ideas for coping mechanisms that they haven't thought of yet, as well as acceptance after a life of feeling rejected and completely alone.
I joined a Discord server for autistic and ADHD folk that has a healthy mix of formally- and self-diagnosed people back at the beginning of my "research/maybe" phase, and in the couple of years between my epiphany and formal diagnosis my life was radically changed by a) realising I wasn't an aberration/the only one, and b) getting tips and ideas from those who'd gone before.
For autistic adults in the UK, we all know there's nothing remotely resembling state support anyway. However, that's not the only support that can be useful (thankfully).
Anyway, to answer the original question...the "explosion" in diagnoses can mostly be explained by the fact that there are currently several generations of people suddenly making the realisation that they could be ND rather than just broken (and the consequences of that actually increase with age for those of us who learned to mask early and thus slipped through unnoticed - it gets harder and harder to keep up the pretence of being typical as we get older). Give it 20 years or so, and it'll even out.