The vaccine rollout was indeed successful.
Their handling of the entire crisis up to that point was little short of a disaster though, as reflected in the relative death tolls. If the perception within the UK is that the government largely did well (bar one or two issues) then (as
@Pexbo &
@Balljy alluded to above) that speaks to a problem with the information people within the UK are being fed.
Because from an outside perspective, the UK government's response was a shit-show. And that perception is the one that's backed by the data.