Video report by ITV News reporter Romilly Weeks
But the prime minister said he is "very optimistic" that he can stick to his plan that he hopes will see almost all of society reopened and a removal of all social restrictions.
Speaking at a school in south London, the PM told reporters: "I'm hopeful but obviously nothing can be guaranteed and it all depends on the way we continue to be prudent and continue to follow the guidance in each stage.
"Genuinely because of the immense possibilities of the [vaccine] rollout, because science has given us this way of creating a shield around our population, we can really look at that June 21 date with some optimism.
"I think that's how I would put it. I'm very optimistic that we'll be able to get there."
The route away from lockdown, as set out by Mr Johnson on Monday, will see schools reopen on March 8, before the rule of six for socialising outdoors returns on March 29 at the earliest.
Then there will be five weeks after the reopening of each sector of the economy, before the final step is completed on June 21 with a final lifting of restrictions that will even see nightclubs reopened - if all goes according to plan.
Each date given on the roadmap is based on the best-case scenario and the prime minister has been careful to warn that every step is subject to delay, if the data suggests necessary.
Downing Street said that June 21 was the "earliest" date for step four - when all coronavirus measures could be eased - after people on Twitter called for it to become a new national bank holiday.
When asked if this was something Mr Johnson would consider, the PM's official spokesman said: "As it says, June 21 is the earliest for step four.
"And as the road map sets out we need to continue to look at the evidence and data as we move through the road map."
Amid criticism from some of his own MPs that the route out of lockdown is not quick enough, Mr Johnson told reporters on Tuesday morning that "the balance is right".
He said: "Some people will say that we're going to be going too fast, some people will say we're going too slow.
"I think the balance is right, I think it is a cautious but irreversible approach, which is exactly what people want to see."
Mr Johnson, when setting out the roadmap in a Downing Street press conference, suggested vaccine certificates - also known as vaccine passports - could facilitate the reopening of some aspects of society, such as the hospitality industry.
Cabinet Office Minister Michael Gove has been tasked with leading a review into the possible use of vaccine passports, the PM said.
"This is an area where we're looking at a novelty for our country, we haven't had stuff like this before, we've never thought in terms of having something that you have to show to go to a pub or a theatre.
"There are deep and complex issues that we need to explore, and ethical issues about what the role is for government in mandating or for people to have such a thing or indeed in banning from people doing such a thing.
"We can't be discriminatory against people who for whatever reason people can't have the vaccine, there might be medical reasons why people can't have a vaccine.
"Or some people may generally refuse to have one, I think that's mistaken, I think everybody should have a vaccine but we need to thrash all this out."
He added: "The fervent libertarians will reject but other people will think there's a case for it."
It had been expected that schools in England would see a staggered reopening, with primaries going first, followed by secondary, then colleges, but the PM opted to let all pupils return on the same date.
He insisted schools are safe and the return of students is "massively important for the country".
The five weeks following each reopening will be used to assess data following the previous step, to decide whether it is safe to proceed with the next.
The PM said that's a "sensible approach, a prudent approach".
"But also as I think people can see it goes on irreversibly and we open up on June 21 in a way that I don't think people would have really thought possible had it not been for the rollout of the vaccinations."
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