The think about the 8,000 figure is it looks to me like a bit of an outlier. On either side of that there's been a fairly reliable c.5,000 increase in cases for a while -- and, besides, the UK isn't the only data set worth studying. You can see similar trends in most European countries.
It's worth stressing that the "advantage" I have over officials is that my judgement is entirely academic. Nobody cares about what I say, meaning I have perhaps a freedom to go further than the official line. As I understand it, there is hope that the lockdown is having an effect but, for obvious reasons, there is much more caution to say so at the top when policy issues are at stake. Nevertheless, I'd say that there are good signs that the lock down is having an effect -- and, of course, extremely good reasons to believe that it would.
// Of course it [followed exponential growth]. It began from zero. An increase from one to two is 100%. From 2 to 8 is another 400%. Small numbers; big percentages. //
I'm not sure how to reply to that because it seems to utterly miss the point. An exponential growth rate is how a disease spreads if it's uncontrolled (at least initially; a more accurate version is the SIR model, but this is exponential to start with before correcting as the disease runs out of new people to infect), and it doesn't rely on small numbers to see that effect. Without controls, and assuming perfect data, then the spread would have continued at essentially the same rate for quite some time.
// My analysis is based solely on the published figures which are for hospital admissions only. People in hospital don’t go there because they’ve tested positive. They go there because they are ill. //
Then shouldn't your analysis also acknowledge an apparent trend towards fewer new cases there, too? The information I understood the government to have released includes, for example, that they haven't exhausted critical care capacity -- which is, not incidentally, the entire point of the lockdown -- and that there are maybe the signs that hospital cases are stabilising.
I just don't see how you can arrive at any conclusion that the lockdown isn't having an impact. Also, as a matter of fact, although yes we can't say for certain what would have happened without a lockdown, the entire purpose of modelling is to understand what is likely to have happened -- and what common sense and mathematical models tell us is that without such extreme measures the disease would be out of control and then some, and the number of deaths and rate of deaths would be much higher. What the actual scale would be I cannot of course say, but I think that at least half as much again by now would be a reasonable ballpark.