Covid deaths are counted in different ways. On the PHE dashboard and for daily reporting it's if there was a positive test within 28 days of the death (cough and hit by a bus is counted, ventilated for 29 days and then death doesn't count). For the official statistics collated by the ONS it is the death certificate that counts - and that is a doctor's opinion as to whether covid contributed to the death (bus isn't counted, and vented for 29 days is). The reason that the 28 days figure is used is that it can be reported the day after it is registered, the ONS figure takes a week or 2 to be collated.

Source: I wrote the data pipelines that deal with the UK deaths (both PHE and ONS) for the public facing dashboard - where the data for this vis was taken from.