New data from NHS England published on Thursday, shows an estimated 20.3% of people in this age group had received both jabs as of March 14.
Some 1.6% of people aged 75 to 79 in England are estimated to have had both doses, along with 0.8% of people aged 70 to 74.
The data also suggests that an estimated 84.6% of people aged 55 and over in England are likely to have had their first dose.
Regional estimates range from 78.6% for London to 87.1% for the Midlands.
The new figures come as all those in England aged 50 to 54 are being formally invited to get their Covid vaccine.
Health Secretary Matt Hancock told a Downing Street press conference on Wednesday that vaccine supply was “always lumpy”, but insisted the nation was on track to meet the target of offering a first dose to all over-50s by April 15.
An estimated 21.8% people aged 16 to 54 in England are likely to have had their first dose of Covid-19 vaccine, the figures show.
The estimates show only small variation between regions, ranging from 18.7% in London to 23.8% in north-west England.
Vaccines have yet to be officially rolled out in England to the general population under 56, but a growing minority of people in this age group are likely to have been offered a dose due to their job or because they have a particular health condition.
All frontline health and social care workers are eligible to receive the vaccine, together with all individuals aged 16 to 64 with underlying health conditions that put them at higher risk of serious disease and mortality.
The figures for vaccinations have been published by NHS England, and they have been combined with population estimates from the Office for National Statistics.
It comes as 23,201,466 Covid-19 vaccinations took place in England between December 8 and March 17, according to provisional NHS England data, including first and second doses, which is a rise of 483,675 on the previous day.
Of this number, 21,886,125 were the first dose of a vaccine, a rise of 392,769 on the previous day, while 1,315,341 were a second dose, an increase of 90,906.
During this period 2,830,881 jabs were given to people in London, including 2,655,890 first doses and 174,991 second doses.
This compares with 4,279,904 first doses and 219,857 second doses given to people in the Midlands, a total of 4,499,761.