I don't think you need a serious scientific study to determine whether or not lockdown brought the benefit of slowing infection rates and reducing hospitalistions and deaths
Before the first lockdown,infection rates were increasing exponentially - with hospitalisations and deaths increasing accordingly
After 3 weeks of lockdown, the infection rates had dropped and in due course so did hospitalisations and deaths
After the easing of restrictions during the summer/autumn,the infection raters again increased exponentially and only a second lockdown combined with the vaccination programme has got us to where we are now - low infection rates. low numbers of hospitalisations and low numbers of deaths.
The government has already announced a public enquiry into how the UK has handled the Covid pandemic and I'm sure the efficacy of the CMO/SAGE advice will be closely examined.
Also, remember that that CMO/SAGE advice to the government does not come with 100% certainty - rather it is given on a sliding scale of probabilities.
It is also only one source of advice on which the government bases its decisions
Cheers
Bruce