No, Public Health England are providing death statistics to the government as and when they receive/can process it - Some of numbers being added to the total today actually died back in mid March
They're NHS England figures, so you need to add on Wales and Scotland, and NI too presumably.
Also, because the numbers in the spreadsheet show date of death, rather than date of publication, they'll be different anyway, but the numbers in the spreadsheet are probably, once they're backfilled, a better indication of the trend.
Are NHS England and Public Health England using the same approach?

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