ds(16) was doing NAT5s this year (GCSE equiv) and is getting some work home which is taking up most of the school day. Ive told him he would have been studying for his exams and this study would not only have been for the exams but also to firm up his knowledge prior which will be the foundation to his Highers (A level equiv) next year. So far he is doing it and it is keeping him more than occupied, but I know many aren't (his physics teacher told them only 12 out of 50 students that are progressing to higher did).
His English teacher has told them to work through past papers and send in for him to mark. Read quality journalism, keep a diary about the lockdown, read books (I think some sites are allowing free downloads just now).
Outside of ongoing school work he is walking the dog with me, he is doing exercises at home (weights, skipping, etc), helping with more chores/cooking. This weekend if the weather keeps up he will be helping in the garden this afternoon.
Add in a board/card game night a couple of times a week and although we are missing outdoors we are keeping reasonably occupied.
I am WFH so I am also keeping busy. We have a bigger problem with dh who can't go out to work and struggles to find ways to keep himself occupied!!!
If your boys are year 11 (is that GCSE year?) why isn't their school providing work? If the school isn't providing work what are their plans for next year? If they aren't leaving school they can still study their subjects to put them in a good place for starting A levels next year. If they are leaving they can start studying their college subjects.
You are right, 6 months of doing nothing wont be good for them so you need to motivate them now before they settle into that pattern.