In Tokyo we have some low-cost international schools that cost about 1/3 of the full-price regular international schools.
They were set up originally by Indian incomers who were middle class (usually software professionals) but lacking in the fat expat packages that some expats have, so they really needed English-medium education at affordable prices. Nowadays, children from a variety of backgrounds also attend.
The facilities are limited - very little outdoor space (the one I am most familiar with has the kids play in the public park next-door in lieu of a schoolyard). Academically they are fine. The classes are over 30 and teaching style is very much textbook based (chalk and talk, work through the textbook and workbook) so not much need for lesson planning. Primary classes can therefore be taught by women who are OK with accepting a lower salary in exchange for a family-friendly job. Secondary teachers can teach more periods so fewer will need to be on payroll. I have to report, the DB and iGCSE/A-level results of the schools suggest that it doesn't do the kids any harm.
Someone mentioned schools where there isn't any complex SEN, that will be a factor. But more broadly, a school where all the families can be assumed to be reasonably "switched on" will not need to fulfil the "social worker" role that state schools find hard to avoid. In a school which has to accept every type of family, you kind of have to find ways to get the kids to swimming lessons and sporting opportunities etc. etc., otherwise quite a lot of kids will wind up unable to swim and never experiencing sports or music. If you can assume that the parents are the kind of people who'd put their kids in swimming lessons anyway, there isn't the same need to provide basic input into these areas at school.
I mentioned India, where a lot of the families come from. In India, I think most kids actually go to low-cost private schools, because the Indian government-run ones are like, dire beyond belief. The guy who set up the Durham school actually made his originally career setting up and supporting low-cost private schools in developing and middle-income countries.
I do not think there is much of a need for these kinds of schools in the UK, where the state sector is basically functional. If I was going to suggest a niche need that such schools might fill, I'd suggest a low-cost private SECONDARY (not primary) in London or similar place (densely populated, actual pressure on school places). You do hear of quite a lot of parents getting no place in a secondary school they are remotely happy with, and secondary-level is the point where "bad schools" are not just non-ideal but actually start to be dangerous and scary places that you would really worry about using. Furthermore, kids can commute from various locations across London once they are secondary school aged, meaning you're not reliant on having a particular group of disappointed parents in one single location, unlike with a primary.