My memory has faded a bit on the masks thing for children but, as far as I recall the decision mostly came after a lot of pressure from some lobbying groups who are more powerful in Westminster than their membership numbers suggest they should be. It was never based on any medical reason, just 'they shouldn't have to'. It was also tied up in the 'they don't catch it/transmit/have symptoms' debate.
As far as schools go, the same lobbying group vigorously opposed use. There is no research, actually, not many of the proclamations made about schooling (the two most obvious being forward facing desks and masks). Even in the guidance it says masks could hinder teaching and learning . It is obviously why there is no evidence _ there is no precedent to research from : notwithstanding these educational decisions are often announced as if they are based on weighty research which is why the DfE is always so keen to cite Chris Whitty and 'senior medics'. They have never managed to find a senior educational researcher to agree , possibly again simply because they wills ay there is no research into these things.
I do think masks might become the new sticking plaster at secondary , however, in an attempt to look to be doing something ( a lot of teachers are pro masks, i think, because they want to feel as 'protected' as other workforces, rather than abandoned). I am not convinced that masks will overcome issues of cleanliness, overcrowding and poor ventilation. But then I don't know what the single most important measure is supposed to be, or even whether they can be separated out. I would have thought it would be SD?