The first ONS study of prevalence in schools is out:
www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/covid19schoolsinfectionsurveyround1england/november2020
Whilst they are taking great pains to emphasise this is indicative only, and unweighted, what's interesting is that the overall positivity rate in secondary schools over the period (basically 1.5% for students and 1.5% for staff, 95% confidence interval of 1.09-1.97) is pretty close (well within the bounds of statistical significance) of the overall community positivity rate from the overall ONS studies from the same periods.
Infection rates in primaries were lower - 0.75% of pupils, 0.89% of staff (again pretty wide confidence intervals)
The schools study covers 3-19 Nov; the ONS study covering 8-14th suggested 1/80 in England, or 1.25%, of the community population , had Corona.
Obviously, infections have continued apace since then, so the next publication will be more interesting in terms of how this plays out.
105 schools (63 secondary, 42 primary) in 14 local authorities (9 high prevalence, 5 low prevalence) took part in the first round of testing, hence the emphasis on it being indicative only.