I've seen fanfics that put the number of British magicals as low as 70 - 90K and as high as 1.8m, with the majority being hidden on islands off the coast of Scotland & Wales and some off the coast of Ireland. I've seen writers speculate that there are 20K in the "village" of Hogsmeade and a further 10 - 15K in and around London.
I couldn't imagine there being more than ~10,000 wizards in the British Isles. 4-8 students per dorm at Hogwarts, 8 dorms per year, 200 year mean life expectancy => 10K wizards.
What I've read
felt like a small town. When the cops (aurors) show up, it's always the same handful of faces. The mayor ("Minister for Magic") has that combination of personal charm and incompetence that wouldn't be elected if there were anyone else running for the position. There's only one newspaper. There's only one bank. There's only one bookshop. There's only one wandmaker. There's only one medical facility and it's combined research, treatment and long term care. Inasmuch as there are a handful of places that wizards live together (widely distributed suburbs), only a handful of families are at each location. The 26 Noble and Ancient Houses represent the 1% (and 3-6 living members of the surviving houses would be roughly 100 people, 1% of 10,000).
Where that gets weird is they have textbooks. Written by a
lot of different people. (And only Lockhart of the professors at Hogwarts teaches from his own book.) There are only two English language wizard schools (of the 11 canonical schools in the world), so each textbook has a print run of ~50 copies a year. Less for the electives in the later years. That's vanity printing levels and
should cost upwards of a hundred galleons a copy unless they can cut a corner somewhere (an army of dictaquills and something that turns pages in unison?).
And why is this setup using humans to start with? Make a literal meat puppet and gussy it up with magic, or polyjuice a pig or something and program that to be a doll in the dollhouse. Sure, still moral arguments to be made, but less missing persons that'll raise a fuss.
I just assumed it's cheaper. You have to provide food but she can cook for herself and you don't have to muck out her stall. Polyjuice is expensive. Costly components and a month of prep for a few hours of non-pigdom. (Though given polyjuice exists, I have to assume that there is also a provider of services that lets you customize your experience if you provide the material. Want a night with Rita Skeeter? Amelia Bones? One of the Harpies? Victor Krum? Dumbledore?)
These are the descendants of the wizards that magicked house elves into servitude and made them like it.
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'.
Muggleborn wizards being purely random doesn't reflect that wizards mostly have wizard children? If 1 in 1000 children born amongst the muggle population is a wizard then shouldn't 1 in 1000 children born to wizards be a wizard? [and the other 999 be squibs]. If it has a genetic component, then 1 in 4 wizard-born children being squibs would be reflected with a 1 in 4 chance of a child in a family where both of the parents are related to a squib.
Though 1 in 1000 is
high. That means if you don't personally know a wizard, then you know multiple people who know wizards and you probably went to school with one. That weird kid at your elementary school who kept having accidents and claiming he didn't do it? Wizard.
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.
Or to put it the other way, 1 in 10,000 makes more sense than 1 in 1,000.
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.
I grew up in a town with ~10K people that still had 6 professional football teams and three football fields. The players got a share of the gate, which was only a few dollars. Not enough to support a family (or even the player if they didn't have other work). Still paid. Still technically professional. Quidditch is the
only wizarding sport. They don't have cinemas or computers or any other kind of recreation on a Saturday afternoon. It's quidditch or chess or reading a book.
I'd expect 20-50% of the entire population of Britain to be attending each match just because they have nothing better to do on the weekend, and the travel expense is only a handful of floo powder.
Does Hogwarts have the only quidditch field in the UK? In the seven books of HP, there are only ~30 intra-school/inter-house quidditch matches, and most hopeful players can expect to only play six or so games in their Hogwarts career. I assumed there were 8 or so teams in the "professional" league, (I think there are only 3-4 named in print? the Chudley Cannons, the Holyhead Harpies, ...). 8 teams would be a season of ~100 games which could run for the full year because they're wizards, they don't need to worry about the weather. That's two matches a weekend, and each team plays once a fortnight. Having more than one stadium in the UK would seem excessive?
I've always read JKR as not having the foggiest idea what a galleon is worth. She wanted her wizards to use gold coins with fanciful names, so she gave them gold coins with fanciful names. How many galleons/sickles/knuts for a loaf of bread? a gallon of milk? How many bakers are there in the wizarding world? How many millers? How many wheat farmers? Where do they buy food? If they buy food from the muggles, what do they trade? Is it legal to obliviate a muggle if that means you don't have to pay the clerk at the corner store?
Do wizards pay taxes? If so, do they pay in galleons or pounds? who collects them and why didn't any of the characters in the book complain about the inland revenue? Should Peter Pettigrew have gone down for tax evasion? If not, how do any of the public servants (including the professors at Hogwarts) get paid? Are galleons an international currency? How do the goblins avoid the problems that hit Greece when they took on the Euro?
Where are the wizard miners? weavers? real estate agents? lawyers? accountants? tax collectors? why isn't there a wizarding public library?
How much does a dragon eat? How many acres of pasturage do you need to support a single dragon? What's their hunting range? What constitutes a stable breeding population? Are there any left in the "wild"? Are Hungarian Horntail and the other "types" of dragons mentioned in the books distinct species (ie not capable of interbreeding and must be considered separately as to whether they are "endangered") or are they breeds like dogs?
Ditto hippogryphs. Ditto acromantulas. Ditto basilisks. Ditto whatever species Fluffy was.
Fundamentally, JKR was writing a "school" story and people and events outside of the school are not relevant to the story. So if you think that mountain in the background is pretty and want a closer look, be prepared to bump your nose into the matte painting.
