Doghead13
Grumpy Old Scottish Biker
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I've seen a few sources claim that the British magical population is only 3000 individuals, with a third of those being 17 and under.
Rowling was asked something to the effect of, out of all muggles born, how many are muggleborns. Her exact answer was 'about one in a thousand'.
Two minutes on Google shows that in 2017 there were 679,106 children born in the UK. 2017 because that's the first year I saw a stated total for, it's late and I'm not exactly full of beans tonight. Ergo, in 2017 there should have been about 679 muggleborns born in the UK by dint of JKR's 'one in a thousand'. Given what I know of UK population growth trends It follows that there should be about four and a half thousand - one and a half time your stated TOTAL population figure - Hogwarts-aged muggleborns in Britain at the time Harry went through Hogwarts.
I think your estimate may be a little on the low side. I mean really low. Ten tmes that is still lowballed sort of low.
The lowball estimates also fail to make sense in a bunch of other regards; basically, you cannot possibly support what we see in canon outside Hogwarts - the scale of government, the DMLE, Gringotts, Diagon, and most prominent of all Quidditch - with such a small population. You CANNOT support a professional sporting institution of that scale on the population of a one-pub town, it's just nuts; push it up to 30k and it still seems odd. Even if we assume Quidditch is amateur - base it on Shinty, everyone has a day job - you need over a hundred thousand people just to get enough of an audience to take it past 'pub football match', and much the same goes for what little we know of the government and infrastructure of the Wizarding World. It's like Lichenstein somehow supporting an army the size of the entire US military, the numbers just don't work.
Making it all add up is very easy: increase the population and add more schools. A hundred thou is what I'd call the lowball estimate for making Wizarding Britain work; I'm more comfortable with closer to a quarter million. You get one free Hagrid calling Hogwarts the best school of magic in the country rather than the only school of magic in the country making sense into the bargain.