The person who said coronavirus is here now and we can't have a world without it and just carry on is correct. We could stop lockdown, cases will soar, community transmission high, and so staff in NHS/public services will stay home, either sick or to care for other sick family members. Plus consumer confidence is going to be lower anyway, and shopping less tempting, when the risks are higher and the bodies piling on the news.
One of the reasons schools closed when they did wasn't because it was the plan, it was because staff absences made it impossible to keep them open. If you play that out similarly across all other public services, the issue isn't top down policy, it's bottom up high sickness rates (and that's even if you can get over the extreme trauma of working in an overwhelmed NHS system and the deaths that will occur as the system overloads/crashes).
I agree that the counting is important though, and looking at whether death rates are drastically different. One thing to watch is that in both Italy and here there death rates from corona are not properly recorded, so if several people die of corona in an nursing home, as has happened, they may not appear on the stats because they won't be tested. So, community death rates are likely to be important, but it's hard to find info on them. As others have said- looking at rates of deaths due to economic hardship or suicide will also be important- however you have to remember you can't compare this year with a non-corona year really, because corona was here and would be killing quite a reasonable amount of the population even if we didn't do lockdown- so mental health and the economy would have been hit anyway, due to larger amount of deaths, and sizeable sickness in key populations.