We estimate the potential impact of COVID-19 on the United Kingdom economy, including direct disease effects, preventive public actions and associated policies. A sectoral, whole-economy macroeconomic model was linked to a population-wide epidemiological demographic model to assess the potential macroeconomic impact of COVID-19, together with policies to mitigate or suppress the pandemic by means of home quarantine, school closures, social distancing and accompanying business closures. Our simulations indicate that, assuming a clinical attack rate of 48% and a case fatality ratio of 1.5%, COVID-19 alone would impose a direct health-related economic burden of £39.6bn (1.73% of GDP) on the UK economy. Mitigation strategies imposed for 12 weeks reduce case fatalities by 29%, but the total cost to the economy is £308bn (13.5% of GDP); £66bn (2.9% of GDP) of which is attributable to labour lost from working parents during school closures, and £201bn (8.8% of GDP) of which is attributable to business closures. Suppressing the pandemic over a longer period of time may reduce deaths by 95%, but the total cost to the UK economy also increases to £668bn (29.2% of GDP), where £166bn (7.3% of GDP) is attributable to school closures and 502bn (21.9% of GDP) to business closures. Our analyses suggest Covid-19 has the potential to impose unprecedented economic costs on the UK economy, and whilst public actions are necessary to minimise mortality, the duration of school and business closures are key to determining the economic cost. The initial economic support package promised by the UK government may be proportionate to the costs of mitigating Covid-19, but without alternative measures to reduce the scale and duration of school and business closures, the economic support may be insufficient to compensate for longer term suppression of the pandemic which could generate an even greater health impact through major recession.