Canon is fairly clear that Hogwarts is the only game in Britain. It also leads to glaring inconsistencies in scale which you just pointed out. (Rowling originally said that Hogwarts had about 700 students, and then fans started pointing out that that was wildly inconsistent with the school as she described it. And even that’s too small to make things really work).
But the evidence, from HP7 (page 210 of my first-run American hardback copy):
Lupin is talking about Voldemort’s takeover of Wizarding society, to Harry and the others.
“Attendance is now compulsory for every young witch and wizard,” he replied. “That was announced yesterday. It’s a change, because it was never obligatory before. Of course, nearly every witch and wizard in Britain has been educated at Hogwarts, but their parents had the right to teach them at home or send them abroad if they preferred. This way, Voldemort will have the whole Wizarding population under his eye from a young age.”
“Most wizards” in Britain were educated at Hogwarts, and the exceptions were homeschooled or sent abroad. It’s really hard to read that to imply that there’s another British wizarding school anywhere.
Canon is fairly clear that Hogwarts is the only game in Britain. It also leads to glaring inconsistencies in scale which you just pointed out. (Rowling originally said that Hogwarts had about 700 students, and then fans started pointing out that that was wildly inconsistent with the school as she described it. And even that’s too small to make things really work).
But the evidence, from HP7 (page 210 of my first-run American hardback copy):
Lupin is talking about Voldemort’s takeover of Wizarding society, to Harry and the others.
“Most wizards” in Britain were educated at Hogwarts, and the exceptions were homeschooled or sent abroad. It’s really hard to read that to imply that there’s another British wizarding school anywhere.