"Dying with Covid is different from dying of Covid. Lots of "Covid deaths" are people who would have died anyway, and only happen to be infected with coronavirus."
"People who would have been classified as dying of something else are now being reclassified as Covid deaths."
"They just reclassified all the flu deaths as Covid deaths."
"There were 50,335 deaths involving the coronavirus (COVID-19) that occurred between 1 March and 30 June 2020, registered up to 4 July 2020 in England and Wales; of these, 46,736 had COVID-19 assigned as the underlying cause of death." [our emphasis]
Deaths are higher than usual. The statistics clearly show that in total, far more people are dying than in recent years (that is, there is a high number of excess deaths). So it simply can't be the case that deaths that would have happened anyway are being reclassified.
Covid isn't just killing people who were otherwise close to death. A study by academics at the University of Glasgow suggested people who had died of Covid typically had over a decade to live, based on their age and prior conditions. Other researchers have arrived at similar estimates.
The flu has not disappeared. If flu deaths were just being re-classified as Covid deaths, we'd expect to see a far lower number of flu deaths than in an average year. According to the Office for National Statistics, 73,477 people died of Covid-19 during 2020 in England and Wales. In addition, 20,119 people died of flu or pneumonia in 2020 (the ONS lumps these two diseases together in its numbers). That was somewhat lower than the five-year average for flu and pneumonia (28,140). But flu has certainly not disappeared, and the reduction in flu and pneumonia cases compared to the average over the previous five years (8,020) was about a ninth of the number dying of Covid.
Note that the reduction in flu deaths in 2020 was itself probably due to the Covid pandemic: people were mixing far less due to lockdowns and other measures; they were also wearing masks and taking care of hand hygiene more effectively than in a normal year. To put this another way: Covid is so deadly that total deaths are up even though we have reduced deaths from other sources.
Page added on 19 January 2021
Edit 19 January 2021: Corrected a mistake - we referred to flu deaths in point 4 when the ONS statistics are gathered for both "influenza and pneumonia".