For a long time ADHD was ignored or dismissed in the UK as an "americanitis", so it's no surprise that there's a backlog of people who weren't diagnosed in childhood.
[0] https://www.england.nhs.uk/long-read/report-of-the-independe...
In fact the pattern is almost the opposite of what you'd see in the US where it would be hard to get diagnosed with a SpLD and e.g. ADHD was more widely recognised. But the rub lies in the fact that ADHD, ASD and many SpLDs have fairly high rates of comorbidities with one another, to the point where if you've got dyspraxia and no other diagnosable comorbidity, you're actually in the minority of people with it.
In order to cope with this the NHS has spun out much of the ADHD/ASD assessments through the Right To Choose program (well, in England at least, Scotland/Wales/NI are on their own), which means that private companies are being paid by the NHS to make up the shortfall. Ref: https://adhduk.co.uk/right-to-choose/
Some people say some of the private companies are too lenient with their diagnoses. Some people say that the NHS is too strict with their diagnoses. I'm sure the real answer is somewhere in the middle.
As you say, the sharp rise in diagnoses is probably more due to people become more aware, with less stigma attached, and having better access to assessment.
Shit like _Rain Man_ almost 30 years ago or, more recently stuff like _The Good Doctor_ really don't help though, as those just reinforce the negative stereotypes of Autism.
ADHD also has a strong genetic component with heritability around 75% according to various studies. My parents (undiagnosed but one definitely ADD+ASD) have 1/4 children diagnosed (and another 2/4 almost certainly undiagnosed, one neurotypical), and 6/10 grandchildren diagnosed (the other 4 are neurotypical).
Who knows, in 20 years time mainstream schools could have switched from 20% SEND and 80% neurotypical to 80% SEND and 20% neurotypical.