The 28-day figure is not 100% accurate, no -- but it is clear as day that it's overwhelmingly tracking the correct number of deaths. A previous measure, that counted all deaths among all those who have ever tested positive, was discarded for reasons that became obvious over the Summer. Have a look at the graphs, though, in particular comparing the positive cases curve with the tests curve.
https://coronavirus.data.gov.uk/
Visually, there is a striking correlation, especially once the handicap of low testing rates was overcome after the first wave -- the correlation is even more significant once you take into account the approximate two-to-three week gap between initial infection and death -- and that should be enough, frankly, to allay any fears that the scale of Covid is being exaggerated. When also the clear increase over the average total death toll is taken into account, there can be neither any doubt that Covid is causing a significant number of deaths, nor any doubt that the statistics provided are substantially accurate. Maybe a small percentage of recorded Covid deaths were after all due to entirely unrelated factors, but it is not nearly enough to change the picture. It's wholly misleading, therefore, to talk about "significantly weighted statistics which are inaccurate" in this context.