In England, that includes nearly a quarter of the most elderly, vulnerable patients.
Prime Minister Boris Johnson said it meant that within a two to three weeks they should have a "significant degree of immunity" to the virus.
He said there would be a ramping up to get more people immunised - up to 2 million a week.
The ambition is to vaccinate all the over-70s, the most clinically vulnerable and front-line health and care workers by mid-February. That will require around 13 million vaccinations.
He defended the UK's policy of immunising more people with one dose immediately - rather than holding some stock back to give people a second booster shot - in order to save "the most lives the fastest".
US regulators have questioned the policy, saying it is premature without more trial evidence, but the UK's Medicines and Healthcare products Regulatory Agency says it is a pragmatic decision to protect more people.
Both the Pfizer and Oxford-AstraZeneca vaccines require two doses to provide the best possible protection.
Initially, the strategy for the Pfizer vaccine was to offer people the second dose 21 days after their initial jab - full immunity starts seven days after the second dose.
But when approval was announced for the Oxford-AstraZeneca vaccine on 30 December, it was also announced that the policy would now change - the new priority would be to give as many people a first shot of either vaccine, rather than providing the required two doses in as short a time as possible.
Everyone will still receive their second dose, but this will now be within 12 weeks of their first.
England's chief medical officer Professor Chris Whitty told the Downing Street press conference that extending the gap between the first and second jabs would mean the number of people vaccinated can be doubled over three months.
"If over that period there is more than 50% protection then you have actually won. More people will have been protected than would have been otherwise.
"Our quite strong view is that protection is likely to be lot more than 50%."
Asked whether the longer gap could lead to an increase risk of the virus mutating into a version that could escape the vaccine, he said it was a worry, but a small one.
Chief scientific adviser Sir Patrick Vallance said vaccines would probably need to be changed further down the line to continue to be a good match for the virus - but that this was relatively quick to do.
One of the exciting things about the science of the RNA vaccines is that they are incredibly fast to make in response to new mutations, he said.
Never be afraid to try something new…
An amateur built the Ark that lasted forty days and forty nights; professionals built the Titanic that sank.