An estimated 82.3 per cent of people in this age group had received both doses of the vaccine as of April 25.
For people aged 80 and over the figure is 87.1 per cent, while for 75 to 79-year-olds the estimate is 91.8 per cent.
Some 70.8 per cent of 70 to 74-year-olds are also likely to have had both doses.
However, two of London’s boroughs are in the bottom three of England’s local authorities with Westminster ranked worst with just 55.9 per cent vaccinated and Tower Hamlets at third lowest with just 59.8 per cent.
People aged 70 and over were in the top four groups on the priority list for vaccines, with initial doses offered to over-80s from early December.
Second doses must follow within 12 weeks of the first, meaning people in these age groups yet to have a follow-up jab should receive it within the next few weeks.
The figures for vaccinations were published by NHS England and have been combined with population estimates from the Office for National Statistics.
They suggest 30.9 per cent of 65 to 69-year-olds have had both doses, along with 19.6 per cent of 60 to 64-year-olds, 17.3 per cent of 55 to 59-year-olds, 14.7 per cent of 50 to 54-year-olds and 12.4 per cent of 45 to 49-year-olds.
Some 7.9 per cent of people aged 16 to 44 are also likely to have received both jabs.