//When lockdown was imposed here, the infection count was doubling every four days or so.
That suggests that if it had been imposed a week earlier the toll would have been something like a quarter of what it is now. 20,000's not great but it would be a lot better than 75,000.//
That doesn’t follow at all.
//…and I'm extrapolating the death count from the infection count.//
And that’s your fundamental error. The death rate (that is, the proportion of those diagnosed with the infection who subsequently die) is not constant. In fact it’s not even close to constant. In the early days of the pandemic it exceeded 15%. Today it is less than 3%. There’s many reasons for that – more effective treatment for one. But the biggest factor is that in April/May/June when the death rate was 15%, mass testing was not being carried out. It didn’t start until early June. Consequently the infection rate was vastly understated in that period because the only people being diagnosed with the illness were those who ended up in hospital. The vast majority of people who became infected were – and still are – unlikely to need medical treatment. To simply say a lockdown imposed a week earlier in March would have meant the total death toll would be just 25% of what it is today simply isn’t logical.
Nobody in this country had a clue how many people had been infected in the Spring. I would argue that nobody really knows now, though we can possibly make a better guess. Further than that, there is no quantifiable evidence of the effect the Spring lockdown had. You cannot assume that all transmission ceased upon its implementation and you cannot assume that all the reduction in infection rates was due to the lockdown. In fact that would be a very rash assumption because the period of lowest spread was the period the restrictions were most relaxed during the summer. To rely on extrapolation in the way you have you would have to know, at the very least, the infection rate prior to the lockdown and the subsequent rate after it had been imposed. And you don’t.