The time between vaccine doses has been shortened for people aged over 50 and the clinically vulnerable – from 12 weeks to eight weeks.
It comes amid concerns over the India variant of the coronavirus, with Prime Minister Boris Johnson warning during a news conference of "serious disruption" to the roadmap out of lockdown if the strain shows high transmissibility.
The number of cases of the strain has more than doubled for two weeks in a row in the UK, going from 202 to 520 to 1,313 in a fortnight.
Chief medical officer Professor Chris Whitty said he expected the variant to become the most dominant in the UK.
Some 36,115,955 people have had a first vaccine dose, while 19,319,010 follow up jabs have been administered.
Mr Johnson said: "Following advice from the Joint Committee on Vaccination and Immunisation, we will accelerate remaining second doses to the over-50s and those clinically vulnerable right across the country so they are just eight weeks after the first dose, and if you are in this group the NHS will be in touch with you."
He added: "We will also prioritise first doses for anyone eligible who has not yet come forwards, including the over 40s – and I urge anyone in those groups to come forwards as soon as you can."
The Department of Health and Social Care said in a statement: "This is to ensure people across the UK have the strongest possible protection from the virus at an earlier opportunity."
It added: "Those aged under 50 will continue to get their first dose, with their second dose at 12 weeks, as has been the deployment strategy so far."
Documents from the Scientific Pandemic Influenza Group on Modelling, Operational sub-group suggested that the B.1.617.2 variant has a transmission advantage over the B.1.1.7 strain – also known as the Kent variant.
Other, more targeted, measures will be undertaken in areas which are seeing a rise in the Indian variant.
This includes Bolton and Blackburn with Darwen.
More vaccine centres are being opened, and operating hours are being increased.
Earlier today, the UK reported another 17 coronavirus deaths and 2,193 cases.
Health Secretary Matt Hancock said: "It’s vital we do everything we can and use every resource we have to ensure we continue to keep the nation safe. We have implemented measures at record pace to get on top of this new variant and control the spread.
"Everyone has a role to play in this effort – accept the invite to get a jab when it comes, and if you live in one of the areas where we’ve introduced surge testing, get your free PCR test. Let’s work to fight this together."