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Background: This paper describes a model for estimating COVID-19 related excess deaths that are a direct consequence of insufficient hospital ward bed and intensive care unit (ICU) capacity.Methods: Compartmental models were used to estimate deaths under different combinations of ICU and ward care required and received in England up to late April 2021. Model parameters were sourced from publicly available government information and organisations collating COVID-19 data. A sub-model was used to estimate the mortality scalars that represent increased mortality due to insufficient ICU or general ward bed capacity. Three illustrative scenarios for admissions numbers, 'Optimistic', 'Middling' and 'Pessimistic', were modelled and compared with the subsequent observations to the 3rd February.Results: The key output was the demand and capacity model described. There were no excess deaths from a lack of capacity in the 'Optimistic' scenario. Several of the 'Middling' scenario applications resulted in excess deaths-up to 597 deaths (0.6% increase) with a 20% reduction compared to best estimate ICU capacity. All the 'Pessimistic' scenario applications resulted in excess deaths, ranging from 49,178 (17.0% increase) for a 20% increase in ward bed availability, to 103,735 (35.8% increase) for a 20% shortfall in ward bed availability. These scenarios took no account of the emergence of the new, more transmissible, variant of concern (b.1.1.7).Conclusions: Mortality is increased when hospital demand exceeds available capacity. No excess deaths from breaching capacity would be expected under the 'Optimistic' scenario. The 'Middling' scenario could result in some excess deaths-up to a 0.7% increase relative to the total number of deaths. The 'Pessimistic' scenario would have resulted in significant excess deaths. Our sensitivity analysis indicated a range between 49,178 (17% increase) and 103,735 (35.8% increase). Given the new variant, the pessimistic scenario appeared increasingly likely and could have resulted in a substantial increase in the number of COVID-19 deaths. In the event, it would appear that capacity was not breached at any stage at a national level with no excess deaths. it will remain unclear if minor local capacity breaches resulted in any small number of excess deaths. [ABSTRACT FROM AUTHOR]