I came to say similar to @LuluJakey1 - lots of schools have very vulnerable children, and whilst I agree with proactive closures in theory (although I do think it has to be timed correctly), I worry that these children:
a) won't be 'seen' for several weeks - schools put a significant amount of preparation for summer holidays, when they won't see students for 6 weeks, by contacting relevant agencies to ensure there are even scant 'checks' on at risk children.
b) for a lot of vulnerable children, school is the only consistent, reliable factor in their lives
c) lots of schools make arrangements for charitable support, or liaise with food banks, to provide support for FSM children over holidays - could this be put in place at short notice for a closure of 4 weeks or more?
I'm not negating the need to preemptively close schools/universities, but I do think it needs to be done at the best time to help combat the peak in cases, and that there needs to be some thought about vulnerable children and the effects on them.
On a different note - increasing class sizes is fine in theory (to keep schools open), but it will being its own problems. Put 45 10/11 year olds in a classroom with 1 adult, and you're likely to have a loud, albeit manageable, room; put 45 4/5 year olds in a classroom with 1 adult, and you're close to an accident waiting to happen. Both scenarios are basically babysitting, as no meaningful learning happens in either case.