They really need to clarify the situation where there are two parents and one is a key worker. It would be ridiculous to keep sending children in where there is a stay at home parent, for example.
I really don't know how they could make it clearer to be fair.
"Many parents working in these sectors may be able to ensure their child is kept at home. And every child who can be safely cared for at home should be."
"If it is at all possible for children to be at home, then they should be."
"Children with at least one parent or carer who are identified as critical workers by the government can send their children to school if required."