Update: Today, there were 641 hospital deaths announced for those testing postive for Covid-19 to bring the total up to 18,738

A cautious estimate of the total number of UK excess deaths linked to coronavirus stands today at

44,100

If the Public Health England estimates for all cause mortality in week 16 are correct (they do not have full data yet), this would be in line with the numbers coming out of my updating model.

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/880812/Weekly_report_mortality_w17.pdf

Methodology is here https://twitter.com/ChrisGiles_/status/1252841436317315072