Boris Johnson pledged a massive step-up in daily vaccinations and insisted the UK has enough supply to protect 14 million people by February 15.
At a Downing Street briefing, he also announced the three types of location people would receive their injections – via GPs, hospitals or large vaccination centres at locations such as sports stadiums. He said it meant everyone should be able to get a vaccine within 10 miles of their home.
He said the Army had been brought in to assist with the logistics and would use "battle preparation techniques" to keep up the pace of the campaign.
A further 1,162 Covid-related deaths were announced in the UK on Thursday, the second highest day throughout the pandemic. The highest day was April 21, when 1,224 deaths were recorded. Daily infections fell from over 60,000 on Wednesday, to 52,618.
Sir Simon Stevens, chief executive of the NHS, said 800 people were being admitted to hospital across the country each day, enough to fill a large hospital.
He said there were 50 per cent more coronavirus inpatients in England’s hospitals now, compared with during the peak in April, affecting every region across the country.
The Prime Minister said almost 1.5 million people had been vaccinated against the disease and the Government intended to give everyone in care homes a dose by the end of January.
He stressed the NHS was ready to administer vaccines as quickly as they could be supplied.
The Prime Minister admitted there would probably be "difficulties" in administering the vaccine, but added: "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.
"Of course, there will be difficulties. Appointments will be changed but … 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."
Mr Johnson’s comments came after family doctors experienced problems getting supplies of coronavirus vaccines for their patients.
The "teething problems" risk causing disappointment for vulnerable people who are at the front of the queue to receive the jabs, the Royal College of General Practitioners chair Prof Martin Marshall said.
The comments came as Health Secretary Matt Hancock launched the mass introduction of the Oxford-AstraZeneca Covid-19 vaccine to GP surgeries – but heard first-hand about the issues they face.
The surgery Mr Hancock visited to launch the programme had not received an expected delivery of the Oxford vaccine, which is easier to distribute than the Pfizer-BioNTech drug, which has to be kept frozen.
The need for the rapid implementation of the vaccine was underlined as hospitals across the UK faced rising numbers of seriously-ill patients.
Vials are being delivered to sites across the country as the Government attempts to offer a vaccine to more than 13 million people in the top four priority groups by mid-February – so far 1.3 million have been injected.
Prof Marshall said GPs had already vaccinated hundreds of thousands of patients in the community using the Pfizer product and the Oxford vaccine should allow a greater number of people to be treated in a shorter space of time.

But he added: “Preparing for a vaccination clinic is no easy feat, it involves meticulous planning. Having to change these plans with little notice is frustrating and demoralising for GP teams – not to mention confusing and disappointing for patients.
“A vaccination programme being delivered at this pace and scale is bound to face teething problems.
“It’s vital that GPs and their teams on the ground, running vaccination clinics, are communicated with clearly and listened to – and that any concerns they have about the roll-out are taken seriously, so that they can be addressed.”
That message was underlined to Mr Hancock on a visit to the Bloomsbury Surgery in London, where an expected delivery of the Oxford vaccine was delayed.
Mr Hancock said Britain's move to delay the second doses of Covid-19 vaccines would help to save lives as more people would be able to get some initial protection, defending a policy shift questioned by some scientists.
The abrupt change of tack on December 30 meant people who had been due to receive their second vaccine doses had their appointments cancelled in favour of scheduling more initial shots for others. Some scientists expressed doubts about the decision to alter proven dosing regimes.
Mr Hancock defended the move, saying partial protection for more people would do more good than full protection for a few.
"The justification is really clear and straightforward, which is that it saves more lives, and ultimately, that is the public health justification," Hancock told Parliament.
"The data show that there is a significant protection from both the Oxford and the Pfizer jabs after the first dose."