The 3,910,086 doses administered in the seven days to the end of 22 May was the second highest figure recorded in a comparable one-week period since the vaccination campaign began last December.
A total of 1,370,327 people received a first dose of COVID-19 vaccine and 2,539,759 a second dose in the seven days from Sunday 16 May to Saturday 22 May.
A total of 762,361 doses were administered on 22 May alone - the second highest figure recorded for a single day, with the 556,951 second-dose vaccinations on that day marking a new record high.
A marked acceleration in the vaccination campaign came as offers of jabs were extended to patients aged 32 and 33 years old from 23 and 24 May.
The increased speed of vaccine rollout comes just days after deputy CMO Professor Jonathan Van Tam told a Downing Street briefing that the UK faced a 'straight race' between the transmissibility of the so-called Indian variant of coronavirus - B1.617.2 - and the vaccination campaign.
More than 60m doses of vaccine have now been administered in total in England, including nearly 38m first doses and nearly 23m second doses.
This means 72% of the UK adult population has now received a first dose of vaccine - and 43% has been fully vaccinated with two doses.
More than three quarters of vaccinations in England have been delivered by GP-led teams in primary care. NHS England chief executive Sir Simon Stevens thanked staff involved in the vaccination campaign - calling the rollout of the COVID-19 vaccine in the UK 'one of the greatest achievements' in NHS history.
Mr Stevens said: 'This latest milestone in our ongoing fight against COVID-19 is another opportunity to thank everyone again working throughout this weekend to deliver the NHS COVID-19 vaccination programme come rain or shine, through thick and thin - undoubtedly one of the greatest achievements in health service history.'