The Chris Giles tweet is a fail
He doesn't understand that he is comparing apples with pears.
The NHS England stats published on 5 April (why is he tweeting this today? update the data) are the NHS death reports to 5pm 4th April and the reports made on 4th April could refer to ANY date up to 4th April.
The gov uk stats are simply 'today's reports less cumulative reports to yesterday'. They can't be anything else because nobody wants to constantly re-evaluate.
He appears to be arguing that '27th March's death reports' is the same as '27th March's deaths' .
27th March's death reports were never 27th March's deaths, they were mostly 25th, 26th, 27th.
NHS England first released the 'date of death stats' on Friday.
AFAICT Wales (Scotland is not that important in that it's not included in 'ONS weekly death all causes' releases) still doesn't do that.
He thinks this is an issue, but it's not. Once you smooth out daily variations due to Sundays etc., the release on Friday is mostly deaths that took place on Tuesday and Wednesday, etc.
It doesn't really matter at all that there is a long tail of old deaths in the reports, as the data from today are 95% within the last 7 days, and 70% within the past 3 days. If you treat it as 'two or three days before publication' then that's more than good enough. It won't cause you to 'miss the peak', you just need to look at trends over three or four days - if they are declining, then we past the peak (deaths) that many days ago plus 2/3 days. Easy.
Much more important in any case is 'excess deaths', which we won't know for several weeks..... His graphs don't show us anything particularly interesting. Just keep comparing daily death stats over a rolling 3 day period. No problem.