“Less Chumras: In the UK the government pays for yeshiva education which is why I heard some non-Jews sued to get into a yeshiva a few years back.”
Not really. Yeshivas (= chareidi schools) are typically private or voluntary-aided in which case they have 100% control on their admissions except that it must be published and fair, but can include that you only eat glatt, or have no TV or whatever. Voluntary-aided schools do get state funding which doesn’t cover kodesh staff.
Even state-aided schools can set their admissions criteria to exclude goyim as long as it’s religion-based, not race based.
It’s “free schools” – a third category of which there are only 1 or 2 MO-type schools that have to accept 50% goyim if they don’t have enough yidden applying.