As 1600 people die each day in the UK, the vast majority will have had the vaccine.
They will have died after the vaccine, not necessarily from it.
Whilst I am a pro-vacc, that needs statement needs to be qualified a little...
When they say 1600 or 1559 died from the vaccine, I am sure they will have checked and be fairly sure it was as a direct result of having had the vaccine. As trazor suggests, most of the people who have died recently, will have in fact had the vaccine. All that needs to be considered is the number who have died without having the vaccine, versus the number who have died as a direct result of them having had the vaccine in time to prevent, or reduce the effects of the covid.
A further consideration to take into account, is the number who have had covid, survived it, yet being left crippled with 'long covid' - which is turning fit, healthy young people into living, crippled wrecks.