ONS figures are the gold standard, as they go by registered deaths and have more data than PHE daily reports.
From their figures, the 28 days under-counts and the 60 days over-counts, see attached chart 1
The previous PHE over-counting is still much less than their earlier gross under-counting, see chart 2
Office for National Statistics (ONS)**@ONS
In England, of all deaths that occurred up to 7 August (registered up 15 August), 49,318 involved #COVID19
For the same period, @DHSCgovuk reported 36,645 COVID-19 deaths (where the death occurred within 28 days of receiving a positive test)
http://ow.ly/u3q650B2bZT