I think there are only two consistent bases for data relating to Covid, depending on what you are doing.
If you want to look at trend data for the UK, you really need to look at the ONS data 'by date of death' released 10 days in arrears every Tuesday (and even then the last few days of that is subject to some change). If you want to compare across different countries, then use the 'Total Excess Deaths published' in the FT each day (but updated by different countries on different days).
Individual countries methods of counting (including the UK daily figures) have been subject to interpretation and change depending on what the government thinks at the time and as such, are very difficult to draw conclusions from, particularly in relation to the most recent few days/weeks.
And obviously HWT's stats which are intended to measure a different set of trends entirely.
Spot on! ONS data, now we have some, is the best indication of where we have been, and my stats may give other info.