To be clear, the UK entered a lockdown excluding schools on the 5th of November.
Within a week, positive tests started declining significantly. The lockdown ended on the 2nd of December.
Within a week, positive tests started going up again.
https://www.theguardian.com/world/2020/dec/08/covid-cases-an...
There is plenty of evidence that lockdowns do work. Whether they make sense from an economic or overall quality of life perspective is a separate issue. But they work.