There will be incidental cases of people dying in accidents who have the disease but if a consultant is certifying a death they or the coroner will decide whether the corona virus has contributed to the death or not. If someone is profoundly hypoxic because of corona virus and dies of a beart attack then 1a (cause of death) will be recorded as myocardial infarction whilst corona will be recorded in section 1b (directly caused by) or 2 (a significant condition contributing to the death) on the form. The distinction with or of does not occur when counting corona deaths.
Maybe we should get UK Body Count to ajudicate on the mortality by counting only the deaths reported in newspapers of people who died of rather than with COVID if that makes you feel better.
The official death count will likely be an undercount because of all the elderly people who have and will die at home for whom there is no reliable witness.