Phase 2 of the plan included the remaining sections of the public; around 21 million people.
The government is aiming to offer vaccinations to around 15 million people in the United Kingdom - the over-70s, older care home residents and staff, frontline healthcare workers and the clinically extremely vulnerable - by mid-February.
The next few weeks will be "the worst" of the pandemic for the NHS, he said.
The Department of Health said there will be capacity to deliver "at least" two million jabs per week in England by the end of this month, with staff and residents in care homes offered a vaccine before February.
It means that across England the true number of people infected to date may be five times as high as the total number of known cases according to the government's track-and-trace programme. "This is an appalling situation", he said.
Nurseries should probably close, Starmer said.
The health secretary was speaking amid continued speculation about whether England's third lockdown could be strengthened. Reports suggested that measures could include a ban on exercising with those outside your household, the end of support bubbles, making office workers wear masks and stricter rules for supermarkets such as one-way systems and masks for outside queues.
The next few weeks will be the worst of the pandemic for the National Health Service (NHS), he told the BBC, urging the public to minimise all unnecessary contact with others.
Health Secretary Matt Hancock
Whitty, a regular at the No 10 press conferences but not someone who often gives interviews, is expected to stress that the risk from social contact is much greater than it was during the first lockdown because the new variant of the virus is so much more transmissible.
Prime Minister Boris Johnson has warned the government "may have to do more" if ministers feel the rules "are not being properly observed".
But with all centres, people will need to wait until they receive an invitation. If an appointment has already been offered by the GP, people can choose which appointment suits them best.
More than 370,000 people in England have received two doses of a Covid vaccine, according to NHS data, despite ministers and scientists previously saying that first doses were going to be prioritised.
Officials have faced increasing calls for frontline workers outside of the NHS and care work - including teachers, transport workers and first responders - to also be vaccinated.
As Britain gears up to rush out its largest vaccination programme with shots offered to more than 15 million people by mid-February, Johnson said, "It's a race against time because we can all see the threat that our NHS faces, the pressure it's under, the demand in intensive care units, the pressure on ventilated beds, even the shortage of oxygen in some places".
"And it's very important we actually vaccinate the maximum number of people over this really unsafe period over winter - the next few weeks, which are going to be the worst weeks of the pandemic in terms of numbers into the NHS, we must be vaccinating as many people as we can".
This would account for nearly half of the priority groups in phase one, with all 9 high-risk groups for phase one of the programme being vaccinated by spring.