@TheTurn0fTheScrew
I don't think this is a universal policy. DC1 had a heavy cold in the Autumn - very snotty, catarrh, watering eyes, but no cough or temperature. School were entirely comfortable with her being in.
Most schools would, and should, admit a child with these symptoms in, as they don't have one of the 3 main covid symptoms.
Though an obviously ill child is better at home, if they are also feeling poorly with their cold.
However, if a child has a cough or a temperature with their cold they should be off until they receive a negative pcr result. Even if you don't think it's covid children should be following the same rules as adults. And even if the cough doesn't last all day, or the temperature is t sustained.
I am pretty sure this is how I picked up covid. I ended up in hospital needing treatment, have long covid 7 months later and ongoing medical treatment probably for life now.
The children I taught had 'a cold' - parents subsequently tested positive too. Most of the children were never tested.
My cough was not sustained or continuous really, it was barely a cough - it was like clearing your throat.
My temperature raised to just under 38, for an hour or two. I only know of this as I was being monitored throughout the day and night in hospital. I didn't feel hot at any point.