The BBC's headline is: Covid: UK vaccine rollout 'breaking link' between infections and death.
Seems plausible to me. I took the stat's on new daily cases and new daily deaths from Worldometers.info, overlapped them and shifted deaths back by about two weeks to get the best match. The brown line for 'deaths' is clearly dropping much faster than the blue line for 'cases':
Obviously, neither case numbers nor death numbers are accurate in absolute terms, but as long as the stat's are compiled consistently, the trend is reliable.
Interestingly, assuming the stat's to be reliable, the death rate appears to be about 2.5% (much higher than often assumed) i.e. if there are 1,000 new cases today, there will be 25 new deaths today in two weeks (or whatever the lag is between diagnosis and death).