The absence of data on the current situation in UK schools is what is worrying staff, and some parents.
The only study taking place as far as we know is the Bristol one, which isn't scheduled to release results until well into next year, here:
www.bristol.ac.uk/news/2020/september/commins-study.html
Extract (underlining is mine):
Ensuring pupils and staff stay safe when they return to school this autumn is a major challenge because there is very little scientific evidence on the incidence and transmission of COVID-19 within schools. A ground-breaking research project will test whether 5,000 staff and pupils have active or past COVID-19 infection, develop systems to help schools prevent and cope with an outbreak and assess strategies to support the mental wellbeing of the school community now and moving forward.
The project, COVID-19 Mapping and Mitigation in Schoolsls_ (CoMMinS), will be led by the University of Bristol and is funded by a £2.7 million NIHR-UKRI COVID-19 rapid response initiative.
Around nine million 4- to 18-year-old children attend school in England, around 16 per cent of the total population, but little is known about the impact and transmission patterns of COVID-19 in schoolchildren, how patterns of infection amongst pupils might impact the wider community, or the long-term consequences of school closure on the health of pupils.^
Limiting transmission of coronavirus in schools is challenging because children with COVID-19 often show no obvious symptoms and schoolchildren normally interact with a large number of other children and adults.
Working with Bristol City Council, Public Health England, local primary and secondary schools and other city stakeholders, CoMMinS will, over a six-month period, test for infection in schools and test whether staff and pupils have current or past COVID-19 infection.
Another complementary part of the project will be a collaboration with Middlesex University in a study of wastewater from school drains to monitor the amount of SARS-Cov2 virus present to see if this can provide an early warning of changes in infection levels.