A total of 1,008,472 appointments were arranged over Friday and Saturday through the booking service, NHS England said – an average of more than 21,000 every hour, or six every second.
The true figure is likely to be higher as it does not include appointments at local GP-led vaccination services or people getting the jab at walk-in centres.
The NHS has now administered around 62 million doses since Margaret Keenan became the first member of the public to get a jab on December 8.
Four in five adults have now received their first vaccination, according to NHS England figures, with three in five having both.
Public Health England’s Covid-19 director Dr Susan Hopkins said on Sunday she hoped all people over 40 could get their vaccine before the full easing of lockdown restrictions planned for July 19.
People over 40 are now being contacted to bring forward their second jab in line with update guidance from experts.
Sir Simon Stevens, NHS chief executive, said: “The NHS Covid-19 vaccination programme is gathering momentum as the finishing line comes into sight.
“It is fantastic to see so many young people coming forward to do their bit in the battle against the virus, protecting themselves, their friends and their family – over 3.5 million people under the age of 30 have already had a first dose.”
All adults can book a vaccine at one of the 1,600 vaccination centres, pharmacies or GP clinics available through the national booking service.