Deaths peaked on 8th April, which supports the conclusion that infections peaked about a week before lockdown.
https://twitter.com/ProfKarolSikora/...04040588951554
I posted about the Bristol University study on 24th June, which indicated this. That makes sense, since by a week before lockdown, people were changing their behaviour. Many office workers were already working from home, football matches and other mass gatherings had stopped, shops had signs encouraging social distancing and less people were going to pubs and restaurants - they were finally ordered to shut the Friday before lockdown.
My running club has cautiously started up club nights again (I went down on Tuesday). I was looking at the website the other day and noticed a statement from 17th March, which had said club nights were stopping with immediate effect. So I think that illustrates the general mindset at the time. Lockdown merely took things a few notches further.
Looking at the graph you posted, we don't see any of that. Apparently infections rose at their sharpest in the days before lockdown before miraculously shrinking the moment lockdown is announced. So at the point of lockdown, the number of new infections infections is seemingly running at 550,000 but two or three days later this has fallen to 150,000. This is not remotely supported by the death statistics since deaths have only fallen gradually in the last few months.
If I was being cynical I might conclude that the "well known statistical methods" you think they have used might be termed "making it up". But I'm happy for you to show me a more rational scientific methodology for the graph.