People in this group will be invited by text over the coming days, leaving only adults between 18 and 29 awaiting an invite to come forward.
Patients in England aged 32 and 33 were offered the chance to book their vaccines at the end of last week. Since NHS England opened up vaccination to people in their thirties on 13 May, nearly 4m appointments have been booked.
People aged 39 and under who are eligible, and pregnant women, are being offered the Pfizer or Moderna vaccine in line with recently updated JCVI guidance.
UK-wide almost 38.2m people had received a first dose of the vaccine and 23.2m had received a second dose as of 24 May. In England, GP-led sites have been responsible for giving around three quarters all of jabs.
> Map: Which CCGs have the highest COVID-19 vaccine coverage?
> Keep tabs on the COVID-19 vaccine campaign: GPonline vaccine tracker
Last week Northern Ireland announced that people aged 25-29 can now book COVID-19 jabs, although appointments available each week are limited. Meanwhile Cardiff and Vale University Health Board in Wales has set out plans to offer its entire population aged over 18 a first dose of vaccine by 30 May.
NHS England's national medical director for primary care Dr Nikki Kanani said: ‘Getting the vaccine is the single most important step we can take to protect ourselves, our families and our communities against COVID-19 with the jabs saving thousands of lives already.
‘The offer of a vaccine doesn’t expire so if you are eligible and haven’t booked please do come forward when you’re invited to.’
Health and social care secretary, Matt Hancock said: ‘Our vaccination programme is moving at such a phenomenal pace and I am delighted that less than six months after the first jab [was administered in the UK], we are now able to open the offer to everyone in their thirties and over.
‘I want to say a huge thank you to everyone who has rolled up their sleeves to help us roll out this life-saving jab. The NHS is booking record numbers of appointments and it is fantastic to see the public come forward in such exceptional numbers.’
Rececnt figures show just how rapidly the vaccine is being deployed. UK-wide a total of 3,910,086 doses were administered in the seven days to the end of 22 May - the second highest figure recorded in a comparable one-week period since the vaccination campaign began last December. This means that one in 13 UK adults received either a first- or second-dose vaccine during that week.
A government report on COVID-19 health inequalities, published this week, found that vaccine confidence has 'steadily increased’ across the population as a whole since December - with 93% of adults reporting 'positive sentiment'.
Vaccine hesitancy remains highest in black or black British adults (30%), despite vaccine confidence increasing in this group from 49% (10 December 2020 to 10 January 2021) to 70% (31 March to 25 April 2021).