The government really needs to spell it out clearly that,other than for vulnerable children, the places in school are only available so that critical services can continue to be provided. So they shouldn't be provided for key worker parents who have another adult at home, either working or non-working. The worker in the non-critical role will have to manage the same as other parents who WFH in a non-critical role.
If you are a critical worker working from home but your kids are over, say, 7 and you could take 10-15 minutes out a few times a day to set them up with home learning then you could keep them home. It might be easier for you if you don't, but you could.
There also need to be some onus on employers. Not all roles within the critical worker sectors are essential. Some admin-based or IT-based jobs can be done from home while offering some supervision to children.
And yes, there needs to be obligatory furlough for childcare reasons if needed. There will be some parents of critical workers who are sending their DC in even though they are in a non-critical role at home as they feel they can't meet their employers' demands otherwise.
There is a vaccination programme underway. We need to use the time until the results of that start to take effect to reduce the infection rate by keeping the numbers mixing to an absolute minimum.
The government won't clarify these things though. They will leave schools to try to police things so that parents will be angry at them instead of at the government.