This thread contains anecdotes.
Recent published research in the Lancet (?the best so far) in children 5-17 suggests 1.8% of children have long covid, specifically defined as symptoms lasting longer than 8 weeks.
That is of course a low percentage. Lower than many previous estimates, which fits with people's experiences on this thread ( so the anecdotes fit with the data)
However, a low percentage of a very large number becomes quite a big number, which is how you would get many thousands of children affected. If all the kids 5-17 in the UK were to get covid, and 1.8% went on to get long covid then there would be just under 200k affected, by my reckoning.
Hopefully, that won't happen. However, there are likely to have been thousands affected already (to the extent of symptoms for more than 8 weeks) going by the evidence in the research.
However, people in a low incidence area might not know many children who even got covid. You would be, on balance, unlikely to know a child who had symptoms for more than 8 weeks unless you also knew many dozens of children who had had covid (as only 1.8% have symptoms for that long).
You're right that we don't know how many would have symptoms that persist for longer than 6 months or a year, or how much impact that would have on how people function, which is the important thing.
I don't really like long covid as a term because it is so vague; we don't really understand post-viral syndromes very well.
But I think it merits keeping a watchful eye on how things are going for these poor kids and I'm glad the government has plans for 15 centres to treat them nationwide (you can bet they wouldn't do that unless they thought there was a significant potential issue)