For those talking about people missing out on places etc, you do need to bear in mind the number of 11yos and 4yos isn't static, and in fact has been very much decreasing year on year for a while now nationally. I know this isn't necessarily the same in every part of England, but that is the national picture. A lot of small primary schools around here are having to close classes etc- they'd really welcome additional students, and for some small village schools even 2/3 additional students can actually make a difference!
From about 2012 onwards, the UK birthrate has been falling year on year, so this is starting to impact secondary schools too. Yes, obviously you still get over subscribed schools, but many schools are starting to have less applicants for Y7, which does have a knock on impact higher up the school (until you lose enough students to drop a whole class). So again, these schools may, very well be keen to get additional students and welcome them- the school not having a falling roll is good for everyone!
The only general entry point where this isn't having an impact yet is post-16, but there's always lots of movement post 16, and it is very common for students to move from private to state at this stage anyway and there's usually a bit more flexibility around class sizes at this age anyway, and bigger classes at this level are better for school budgets.
I genuinely don't think schools in my area are worried about accommodating additional students- if anything, they are probably working desperately to recruit them.