Video report by ITV News Political Correspondent Carl Dinnen
He insisted the UK is on target to reach its aim of vaccinating the four groups most vulnerable to coronavirus by mid-February, and a plan for exiting lockdown will be revealed around a week later.
The prime minister said he hopes to announce, in the week beginning 22 February, a "roadmap" which will be used to "reclaim our lives" by gradually reopening schools and the economy in order "to get our lives back to as close to normal as possible".
Mr Johnson admitted the timetable is "inevitably subject to adjustment" and "depends on lots of things going right", particularly the UK's vaccine rollout.
He added: "It also depends on us all now continuing, above all, to work together to drive down the incidents of the disease."
His latest comments on lifting national restrictions come as the UK will follow in the footsteps of Australia, China and New Zealand by enforcing a mandatory hotel quarantine for arrivals on a "red list".
UK nationals and residents returning to Britain from "red list" countries will be forced to quarantine for 10 days in government-provided accommodation such as hotels.
Foreign nationals from 22 countries where new variants have been identified - including South Africa, Portugal and South American nations - are also not allowed entry to the UK.
Ahead of the press conference it was revealed that 7,164,387 first doses of coronavirus vaccine had been administered, with 474,156 of those receiving their second dose.
Based on the latest figures, an average of 412,401 first doses of vaccine would be needed each day in order to meet the government's target of 15 million first doses by February 15.
ITV News Political Editor Robert Peston analyses the latest developments on the lockdown and whether the UK could enter a tier system
The PM, asked why vaccination levels have "dropped a bit this week", said: "Don't forget that these are vaccines that have only just been invented and the batches are only just being approved."
He added: "I think one of the things that we said at the beginning is that there would be bumps, there would ups and downs, particularly in these early phases as production gets underway."
He said free school meal arrangements would be extended through the lockdown, including food parcels and the national voucher scheme, and he announced a £300m fund to help pupils "catch up" through tutoring.
The prime minister insisted schools are safe but said they increase the spread of coronavirus.
"The problem is not that schools are unsafe - teachers and headteachers have worked heroically to make sure they are safe, they are Covid-secure.
"The problem is that by definition schools bring many households together and that contributes to the spread of the virus within the community and drives up the R."
Meanwhile Professor Jonathan Van-Tam, the Deputy Medical Officer for England, said children can get Covid-19 but they don't get very ill.
However, he added the older the children are the more they can transmit Covid-19 to others.
Addressing a whole array of short question and answers about transmission of Covid-19 in schools and between children and teachers, Prof Van-Tam said: "Do children get Covid-19? Yes. Do children get ill with it? Very rarely indeed.
"Do children transmit Covid-19? Yes, but it is a signal predominately towards the upper teenage years. In other words, the more adult-like they become, the more propensity there is to transmit to others."
"Do teachers get Covid-19? Yes. Is it clear that children get Covid-19 from children or from each other? No it is not clear. They could also pick it up from their lives outside of school."
"Could infected children introduce it back in their own households and therefore contribute to R? Absolutely."
The government's Chief Scientific Adviser Sir Patrick Vallance said England's lockdown is working but infections are still "very high".
With one in 55 people current estimated to have coronavirus, the country remains in a "difficult position" he said, but "things have slowed down".
Speaking at a Downing Street news conference, Sir Patrick said: "We are at a position where the lockdowns have worked, they've slowed this down, they've reached a position where it has reached a plateau and is beginning to decline - and we see that in cases, we're beginning to see that in hospital admissions and we're beginning to see that in deaths - but it is early days.
"This isn't coming down quickly, we remain at very high levels and it is going to take weeks for this to come down to really low levels.
"It is important with that, and the rollout of the vaccine programme, we start to see this changing, as the Prime Minister has said, and the vaccine programme should start to kick-in so we can see the effects in the middle of February.
"But I want to remind us all that we remain in a difficult position at the moment and there are still very high levels."