When you see the government’s comparisons of deaths in England between Wave One and now, it's important to remember the former was likely an underestimate due to a lack of testing available at the time.

The @PHE_uk measurement is "deaths within 28 days of a positive test".
In September I looked at the range of recorded COVID-19 deaths from different official sources.

There was a large variance between the @ONS “COVID-19 mentions on death certificate” figures and, in particular, the @PHE_uk “deaths within 28 days of a positive test” measurement. https://twitter.com/fact_covid/status/1310329771126140928
Given the flawed nature of the 28-day measurement, which does not take into account the relative shortage of testing available earlier in the year, and records deaths within that time period regardless of cause, the @ons figure is arguably more reliable.
To clarify, the @ons figures are those deaths registered in England where COVID-19 was mentioned on the death certificate.

A doctor can certify the involvement of COVID-19 based on symptoms and clinical findings - a positive test is not required.
It’s likely hospitalisations were also underestimated in March/April, as those reported numbers are specifically people “who tested positive for COVID-19 in the 14 days prior to admission, and those who tested positive in hospital after admission.”
Clearly deaths are increasing, and we expect that to continue for some time sadly, based on all available data.

However the current wave looks less severe in comparison to the first if you rely on the @ONS figures as opposed to the @PHE_uk ones.

Here’s that chart again.
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