Weekly data from the Office for National Statistics (ONS) show there were 84 death certificates mentioning Covid in the week ending June 11.
By contrast there were 1,163 deaths registered involving flu and pneumonia.
In the previous week, 98 Covid deaths were recorded, meaning this week it has dropped by 14 per cent.
Kevin McConway, the emeritus professor of applied statistics at The Open University, told The Telegraph: “The excellent news in this bulletin is that the number of deaths involving Covid-19 actually fell again.
“The numbers are down in most age groups and most regions, comparing the latest week with either the previous week or the week before that.
“Deaths involving Covid-19 made up just eight out of every thousand total deaths in the most recent week.
“It's not good news that the number of infections is increasing, even though it is a little encouraging that the increase in cases hasn't yet led to any substantial increase in deaths involving Covid and, judging by these ONS figures, if anything there's a decrease in deaths.”
Covid deaths now make up just 0.8 per cent of all deaths – down from 1.3 per cent in the week before.
But the figures are lower than would be expected for respiratory disease at this time of year, with the five-year average for deaths involving flu and pneumonia in the same week is 1,704.
Prof Conway added: “I don't think a large increase in deaths is inevitable, given the very encouraging recent data from PHE on the effectiveness of vaccines against hospitalisations involving the delta variant.”
There were only five Covid deaths reported on Monday, despite an increase in cases and hospital admissions.
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