Before revision:  Both the ONS's corresponding count of 36,870 death certificates which mention COVID-19, and the Department of Health and Social Care's hospital-focused count of 29,057 deaths, are appreciably less, implying that their counting methods have underestimated, not overestimated, the pandemic's true death toll.
After revision:  Both the ONS's corresponding count of 36,870 death certificates which mention COVID-19, and the Department of Health and Social Care's count of 33,671 deaths, are appreciably less, implying that their counting methods have underestimated, not overestimated, the pandemic's true death toll.