It will be some time before reopening schools in England (for all children) is practical. They're just starting to do that in Australia, where infection rates are less than one hundredth of those here (with around 10 new cases a day instead of 5000, despite more aggressive testing). But we can think about how that should be done, once infection rates are much lower and a robust test-and-trace system is in place.
It seems to me that the key to doing this with the least risk, and so it attracts broad support, will be collaboration between individual schools and government (and government agencies). Public health teams, including infectious disease specialists, need to go into every school and work out, with the staff (and possibly the parents association), a set of procedures and policies that will allow them to operate as safely as possible. Full social distancing is obviously going to be impossible, but that doesn't prevent other measures for risk reduction being useful.
Now much of this can be centralised, but a lot of concerns are unique to each school. This is most obvious spatially. Each school has different classroom and playground and overall layouts, and thus different patterns of movement during the day. School entries and approaches are also different, which affects the pickup and dropoff crowding, as are catchment housing densities and the ways children get to school.
There's also a lot of variation in demographics. Children may be unlikely to catch Covid-19 (though the evidence on this still seems unclear), but there are some who are immunosuppressed or have other health problems that make them vulnerable, and many live with vulnerable parents or grandparents. Teaching staff face similar concerns. And the numbers involved vary between schools, as do interactions with other vulnerabilities and safeguarding concerns. Early years units are radically different to sixth form colleges!
Provision of resources is going to be critical: personal protective equipment, temporary building works, cleaning services, rapid access to contact-tracing when cases are detected, and so forth. But just as important will be training staff and providing them (and parents) with the information needed to implement policies, national or local, and explaining why they are necessary and why they matter. The entire process needs to be open and transparent -- and some community concerns may be misguided, but they will still need to be addressed.
Unfortunately national government in the UK seems to have an aversion to community collaboration and more generally to investing in people and human resources. Witness the history of adversarial relationships with teachers, police, doctors, and workers generally. And academisation and stripping of funding from local authorities has crippled the logical entity for coordinating this. (Openness and transparency also seem out of fashion and, perhaps as a result of Brexit, the UK government even appears to have broken its traditional ties with the corporate world, with the result that it can't even coordinate industrial policy, contrast South Korea and Germany. But that's another story.)
So what I fear we will get instead are top-down decrees - "schools will reopen on such and such a date", "people over 65 aren't allowed to work as teachers", "masks are banned/mandatory" - without real consideration of how they will work in practice, or proper resourcing to enable them to be implemented. This will come with a mix of coercion (with Ofsted or a similar body doing periodic inspections to ensure centrally-mandated public health policies are being followed), semi-surreptitious "nudges", and unpredictable and unbalanced provision of resources (probably in the form of funding for ad hoc private schemes thought up by people who happen to have the ear of a minister).