When they first said "herd immunity", most people, including journalists, unfortunately nodded like Owl in Winnie the Pooh, and said, "Ah yes, herd immutinoony. Of course." There are two ways to that - have the virus endemic in the population already, or have vaccination at a level that there's nobody to pass it onto. There was no vaccine. So the government's initial "let's go for herd immunity" meant "let's have everybody catch it". Some right wing commentators even evoked the idea of chicken pox parties. But at that stage, with a hospitalisation rate of potentially 15%, and an ICU requirement of maybe 20% of that, you're looking at pushing 3% of the population - potentially 2 million people -through intensive care within a few months, each for likely over a week.
There are, according to a quick scan of some government stats (https://www.england.nhs.uk/statistics/statistical-work-areas/critical-care-capacity/critical-care-bed-capacity-and-urgent-operations-cancelled-2019-20-data/) about 6000 critical care beds in England. You save maybe half if you can protect the vulnerable - though no mention was made of that to begin with. But even without C19, occupation of these beds runs at over 80%, and people won't stop having heart attacks etc ....
The maths here is so obvious. When I heard about the plan, I didn't need to do a calculation to work out that the NHS would not survive on the basis of what we knew, and quite possibly neither would the infrastructure of the country. That it should have even been contemplated as a way forward was a massive demonstration of the incompetence of the government. That they have been allowed to get away with it is a massive demonstration of the incompetence of the media.
I just discovered this as a draft in my blogger account, having written it in the last week of March, and then it having been overtaken by events, so I didn't publish it.