The cost
On the cost side the lowest resources cost is just to count the GDP that would have been produced in 2020 but for the lockdown established in March and assuming the lockdown to be eased from the end of June. This assumes a rapid bounce back by the end of the year so there is no effect on incomes and output from the start of 2021 onwards. That was the scenario envisaged by the Bank of England in their May 2020 assessment of the economic outlook when they put the GDP loss in 2020 at around 14%. The OBR estimate for lost output in 2020, also based on an assumed rapid recovery in the second half of the year, is close to 13%. It seems plausible that a large fraction of these estimates of lost output is due to the lockdown. But even absent a government-mandated lockdown there would have been some reduction in incomes. If the lockdown effect was two thirds of what the OBR and Bank of England suggest is the loss in GDP for 2020 that might imply around a 9% fall in GDP as a direct result of it.   That is around £200 billion.
That 9% of GDP cost is likely to be a low-end estimate of overall costs of the UK lockdown from mid-March to early June as it:
At the high end of the spectrum would be an estimate of 15% of GDP lost in 2020 and lower output for the next few years on top of that as economic activity does not return to normal for several years with some firms permanently damaged by the lockdown and the large rise in unemployment slow to be reversed, even if restrictions are quickly removed from mid-2020. A shortfall of GDP of 15% in 2020; 7.5% in 2021 and 2.5% in 2022 would be at the more pessimistic end of the spectrum for the impact of the March-June lockdown, though for many economists such a figure seems realistic rather than pessimistic. The cumulative lost output would then be 25% of GDP.