Please please please can those parents saying their DC's schools are doing little/nothing SPEAK to the school! You might feel that your complaint will make little difference, but I seriously doubt you'd be the only one.
DH and I are both teachers. I work at an independent secondary school and am teaching my full timetable and doing many of my other duties - I've just got off the phone from doing some careers?advice for one of my pupils, and am killing 5 mins on mumsnet before the next one is scheduled. My school has instructed me to run as normal (but with lots of leeway for some kids that can't complete work right now). My DH has been given no support and no instructions from his (state) school, and they don't have a platform for online learning. It would clearly not be appropriate for him to just start contacting his students unless that was school policy. So SPEAK TO YOUR KID'S SCHOOL! There is a vast difference between what different schools are doing, and teachers will only do what they are told to, because to do otherwise risks putting you on the wrong side of safeguarding policy.
It would also be useful for me to get feedback from parents about what they want. Some parents want more work (to keep their quite motivated kids occupied and educated), some want less because their darling teenagers are..... teenagers. Working parents don't always have the time or energy to battle recalcitrant kids. But I don't know which families fall into which category without them speaking to me.
Personally, I hope my DD (3yo) will be able to see her preschool class before the summer starts. The risk to young children is low, and she misses her classmates terribly. Her class has a teacher who I suspect will shield, but 3 younger TAs, so I hope they will be able to offer some provision.
Regarding second/subsequent waves - we surely won't know when we are approaching herd immunity (yes, I know there's no absolute proof that people become immune, but let's assume that's this virus is similar to most others and that infection means you are less likely to contract it again) unless/until we have wide-scale antibody testing. It's not likely we'll have this for some time, so let's consider both options:
We ARE approaching herd immunity: logically, it would be best to have any second wave during the summer months - lower viral load (UV light, fresh air), fewer other viruses for the NHS to combat. So schools should trial reopening.
We AREN'T approaching herd immunity: then there will be several more waves and will need to have quite strict social distancing for really quite a long time. In which case, do people really want schools to stay closed for another year or more? Is that in the interests of children?