People aged 21 and 22 have now been invited to book their Covid vaccine from today.
It comes after the head of the NHS in England said that all adults in England should be able to book their first coronavirus jab by the end of the week.
Sir Simon Stevens told the NHS Confederation conference on Tuesday that the NHS will "finish the job" of the Covid-19 vaccination programme to the "greatest extent possible" over the next four weeks during the extension of lockdown.
The NHS said that from Wednesday it will contact 972,000 21- and 22-year-olds to invite them to book their vaccination.
This means only 18- to 20-year-olds are left to get the call.
Dr Emily Lawson, lead for the NHS Covid vaccination programme, said: "The largest ever NHS vaccination campaign is in the home stretch of the first dose rollout.
"The vaccine is the most important step you can take to protect yourself, your friends and family so it's really important everybody in the latest eligible groups books themselves in to get their jab and plays their part in this huge national effort."
Health Secretary Matt Hancock said: "We're almost at the final hurdle of offering lifesaving jabs to all UK adults, with both vaccines providing the fullest possible protection against symptoms, serious illness and hospitalisation from this awful virus and moving us a step closer to beating this pandemic.
"I urge everyone aged 21 and over to get your vaccines booked in as soon as possible to not only secure this extra defence for yourself, but to protect your loved ones too."
Cabinet minister Liz Truss today said the Joint Committee on Vaccination and Immunisation (JCVI) was not recommending offering Covid-19 jabs to under-18s.
The International Trade Secretary told BBC Breakfast: "Of course the Government will look very closely at the JCVI's recommendations.
"It is my understanding that they are not recommending the vaccination of under-18s and we will be saying more in due course about that."
In a press conference on Monday, Chief Medical Officer Chris Whitty said the priority was to give all adults a vaccine by July 19, the new date for when restrictions are set to be eased.
The Prime Minister announced on Monday that so-called Freedom Day has been pushed back to allow for more people to get their second jab.
Boris Johnson also said that the vaccine timetable had been sped up so that over 40s would receive their second dose eight weeks after the first, instead of 12 weeks later.
Health Secretary Matt Hancock said: “Second doses are increasingly vital, so this is an incredibly important milestone.
“Day after day, our vaccination programme reaches new heights. With over 30 million people across the UK now receiving a second dose, we are giving the fullest possible protection to our loved ones in the face of new variants.
“The strength of the union has never been clearer than in the UK vaccination effort. All four corners of this country have pulled together for one common purpose – to get the jab and fight this virus.
“I want to pay tribute to everyone right across the country who has answered our call to arms and rolled up their sleeves to get the jab."