We address the question of: 'how many deaths in England and Wales are due to COVID-19?' There are two approaches to measuring COVID deaths - 'COVID associated deaths' and 'excess deaths'. An excess deaths type framework is preferable, as there is substantial measurement error in COVID associated deaths, due to issues relating to the identification of deaths that are directly attributable to COVID-19. A limitation of the current excess deaths metric (a comparison of deaths to a 5 year average for the same week), is that it attributes the entirety of the variation in mortality to COVID-19. This likely means that the metric is overstated because there are a range of other drivers of mortality. We address this by estimating novel empirical Poisson models for all-cause deaths (in totality; by age category; for males; and females) that account for other drivers including the lockdown Government policy response. The models are novel because they include COVID identifier variables (which are a variation on a dummy variable). We use these identifiers to estimate weekly deviations in COVID deaths (about the mean weekly estimate pertaining to the COVID dummy variable in our baseline model). Results from two sets of identifiers indicate that, over the periods when our weekly estimates of total COVID deaths and the current excess deaths measure differ (week ending 17th or 24th April 2020 - week ending 8th May 2020), the former is considerably below the latter - on average per week 4670 deaths (54%) lower, or 4727 deaths (63%) lower, respectively.