
https://coronavirus.data.gov.uk/ shows a high correlation
Just as aside I note they show positive test and death rate as so many per 100,000. If they used percentage it would be 0.0243% and 0.00002% of the population respectively. Not exactly scary. 
I make it 0.0002% per day death rate but your point is essentially true that lockdown + vaccination has got our death rate right down (and as/more importantly the hospitalisation rate).
Just like they were in July last year before the eat to help out initiative etc blew it right back up again. We have to hope vaccination has squashed it for good. Still only half of Brits here have had a jab.
Cyprus death rate at ~3 a day is (only) about 7 times ours per capita, it's their infection rate at ~1% every two weeks and growing that isn't good at all.