Covid vaccinations will start being given to patients from GP surgeries in England as part of the next stage of the rollout of the programme.
GP practices in more than 100 locations will receive their first deliveries of the vaccine later, the NHS said.
Some will start vaccinating on Monday afternoon, with the majority getting under way on Tuesday.
Tens of thousands of people in the UK received the Pfizer-BioNTech jab last week in hospitals.
Like last week, GP practices will prioritise over-80s, along with health and care staff.
Dr Simon Hodes, a GP from Watford who will begin vaccinations on Monday, told BBC Radio 4’s Today programme patients are welcoming their jab offers with “great excitement”.
He said calls to at-risk over-80s showed very few of his patients had worries about the vaccine.
“They’ve been reading the news – they know it’s safe – and they’re keen to have it,” he said.
He added that his surgery has a “military[-style] operation” to ensure doses of the vaccine are not wasted – with a list of health workers drawn up if doses are going spare.
Dr Nikita Kanani, director of primary care at NHS England, urged people waiting for coronavirus vaccinations to be patient.
“There’s a huge range of things that general practices are already doing so if we can ask for people to just wait a moment and wait to be contacted that would be very appreciated,” she told Today.
- Who will get the vaccine first?
- What you need to know about vaccine safety
- How close is light at end of Covid tunnel?
Meanwhile, Business Secretary Alok Sharma told BBC Breakfast arrangements were in place “to make sure the distribution of vaccines is not in any way disrupted” in the event of a no-deal Brexit.
He added that there would be “some millions” of the Pfizer/BioNTech vaccine in the UK before Christmas.
“We are going as fast as we can in terms of the vaccination programme,” he said.
Once the vaccine is delivered, there will be no messing around. GP practices will receive batches containing 975 doses.
These will have been thawed out – they are kept in ultra-cold storage in hospital – which means practices only have three-and-a-half days to use them up.
It will be all hands on deck therefore with GPs, practice nurses and health care assistants working together to vaccinate the over-80s.
The 100 or so practices getting the vaccine on Monday will be followed by another 100 to 200 over the course of the week.
The rest of the network of 1,200 designated practices – each local area has been asked to nominate one practice to deliver the vaccine – are expected to follow in the coming weeks.
But that will depend on supply. There’s thought to be fewer than one million doses of the Pfizer vaccine in the country – although more is due to arrive from Belgium soon.
What could change the whole speed of rollout is approval of a second vaccine made by Oxford University and AstraZeneca.
Regulators are currently assessing the safety and effectiveness of that vaccine, of which there are already over five million doses available.
Care home residents in England are also expected to receive their first vaccine later this week, along with other parts of the UK, the NHS said.
Roll-out to care homes – the highest priority for vaccination – had been held up by strict rules governing the handling of the Pfizer vaccine, which has to be stored at -70C.
But the regulator is expected to give the green light to vaccinators taking the jab into care homes in the coming days.
In Scotland, family doctors are helping deliver the vaccination programme via hospital hubs but England is the first part of the UK to roll out the jab through GP practices.
Prof Martin Marshall, chairman of the Royal College of GPs, acknowledged there were “logistical challenges” to the rollout but said GPs had “an excellent track record of delivering mass vaccination programmes”.
He added: “We won’t be vaccinating everyone all at once – it will be a relatively small number at first – but as long as there is supply, GPs and our teams at selected sites will start vaccinating people this week, starting with our most vulnerable patients.”
He urged people not to contact their GP enquiring about vaccination, saying patients would be contacted when it was their turn to get the jab.
It comes as a further 18,447 coronavirus cases were recorded across the UK on Sunday, along with 144 deaths within 28 days of a positive test. Recorded deaths tend to be lower over the weekend due to reporting delays.
Ministers and experts have warned the rollout of the vaccine does not mean coronavirus restrictions can be suddenly relaxed.
On Sunday NHS Providers – which represents hospital trusts in England – said people must think carefully about the risk of increased social contact over Christmas, despite the rules allowing three households to mix indoors and stay overnight between 23 and 27 December.