Straight from GOV UK this is the guidance -
'There is no need for primary age pupils (those in Year 6 and below) to test.
If the number of positive cases substantially increases in your nursery, school, college, or area, you might be advised to increase the use of lateral flow device (LFD) testing. This could also include advice on the reintroduction of onsite LFD testing;
'If you insist on your child attending nursery, school, or college when they have symptoms, they can take the decision to refuse your child if, in their reasonable judgement, it is necessary to protect other pupils and staff from possible infection with COVID-19. Their decision would need to be carefully considered in light of all the circumstances and current public health advice.'
Increase in testing refers to staff, under no circumstances should an un-symptomatic child be tested and no staff should ever administer a test.
If this has actually happened someone is very deeply entrenched in the shit.