Video report by ITV News Political Correspondent Daniel Hewitt
Every elderly care home resident will be offered a coronavirus jab by the end of this month, Boris Johnson said.
Almost 1.5 million people have been vaccinated in the UK, the prime minister said, adding that the government is aiming to ramp up capabilities to ensure a vaccine is available to people within 10 miles of their home.
He added that the UK has already protected more people from Covid with vaccinations than all the other countries in Europe put together.
Speaking at a Downing Street press conference, the Prime Minister said: "We’ve now vaccinated 1.26 million people in England, 113,000 in Scotland, 49,000 in Wales and 46,000 in Northern Ireland.
"So, all together, nearly 1.5 million people across the UK have now received their first dose and within two to three weeks all of them will have a very considerable degree of immunity."
He said that thanks to the arrival of the Oxford/AstraZeneca vaccine, which can be stored at room temperature, the government are able to "accelerate the pace of vaccination in care homes".
He added: “We’re using that vaccine in care homes for the first time today and by the end of the month we hope to have offered every elderly care home resident a vaccine.”
Mr Johnson said that the most vulnerable groups which the Government plans to have vaccinated by mid-February accounted for 88% of all those who have died in the UK during the pandemic.
He said: "Our tactics are first to use the immense natural capacity of the NHS.
"By the end of the week, there will be over 1,000 GP-led sites providing vaccines, 223 hospital sites, seven giant vaccination centres and a first wave of 200 community pharmacies.
"If all goes well, these together should have the capacity to deliver hundreds of thousands of vaccines per day by January 15 and it is our plan that everyone should have a vaccination available within a radius of 10 miles.
"It follows from that that the limits will not be on our distributional power but on the supply of vaccines, and I have no doubt that we have enough supply to vaccinate these four groups by the February 15 deadline.
"We also have the distributional network to do it and to continue an expanding programme down the priority list."
The prime minister was joined by NHS England chief executive Sir Simon Stevens who hit out at "lies" that hospitals are not under pressure from the rising coronavirus cases.
He said claims on social media that hospitals were empty were an "insult" to staff working in critical care.
"If you sneak into a hospital in an empty corridor at 9 o'clock at night and film that particular corridor and then stick it up on social media and say 'this proves hospitals are empty, the whole thing is a hoax,' he said.
"You are not only responsible for potentially changing behaviour that will kill people but it is an insult to the nurse coming home from 12 hours critical care having worked her guts out under the most demanding and trying of circumstances."
He added: "There is nothing more demoralising than having that kind of nonsense spouted when it is most obviously untrue," he said.
Sir Simon said particular attention would be paid over the next four or five weeks to groups where there has been "some targeted misinformation, including some of the minority ethnic communities across the country who have been really disgracefully targeted with nonsense about vaccination".
He said more than 800 patients a day are being admitted to London hospitals with Covid-19.
"That is the equivalent of a new St Thomas’ hospital full of Covid patients, fully staffed, every day, or a new University College Hospital, full of coronavirus patients every day," he said.
He added the London NHS intended to open the London Nightingale hospital next week as cases in the capital continue to rise.
“The entirety of the health service in London is mobilising to do everything it possibly can but the rate of growth in admissions – that is what collectively the country has got to get under control," he said.
The Prime Minister said there would likely be “difficulties” in the rollout of the vaccine but that the army had been drafted in to assist with set-up.
He said: “Of course in the early phases there is going to be lumpiness and bumpiness in the distribution.
“Today it may be that some GPs aren’t getting the consignments expected. Other GPs are doing an incredible job getting jabs into people’s arms.”
"Let’s be clear, this is a national challenge on a scale like nothing we’ve seen before and it will require an unprecedented national effort," he told the press conference.
"The army is working hand in glove with the NHS and local councils to set up our vaccine network and using battle preparation techniques to help us keep up the pace."
Sir Simon added there will be a “huge acceleration” in the vaccination programme over the coming weeks to meet the 39-day target set by the PM to vaccinate the most vulnerable.
He said they would be increasing the supplies of the vaccine, the numbers of places where it is being delivered and the numbers administering the jabs.
“We need a huge acceleration if we are, over the next five weeks, going to vaccinate more people than we typically vaccinate over five months during a winter flu programme. We have got 39 days to do it,” he said.
He said the “bulk” of the vaccinations would be carried out at GP surgeries and pharmacies, but that the number of hospital hubs and large-scale vaccination centres were also being increased.
The government is aiming to ramp up vaccination capability to around 2 million people a week, so it can reach a target of having inoculated all of the top four priority groups by mid-February.
On Wednesday it was revealed that seven venues dotted around England had been converted into mass vaccination centres, which will aim to inoculate thousands daily.
It is hoped that more than 700 other sites would be delivering vaccines by the end of the week.
Brigadier Prosser, Commander of Military Support to the Vaccine Delivery Programme, said his team is “embedded” with the NHS.
He said his “day job” is to deliver combat supplies to UK forces in time of war, adding: “My team are used to complexity and building supply chains at speed in the most arduous and challenging conditions.”
He added: "The plan has many challenges which are difficult to balance. We need to make sure that every one of you has equal access to the vaccine no matter where you are in England."