The Prime Minister is facing a revolt from his own MPs when the Commons votes on extending coronavirus laws for a further six months later on Thursday.
Mr Johnson is also facing pressure from the European Union over the issue of vaccine supplies, and stressed he "does not want to see blockades of vaccines".
The EU is in an ongoing dispute with AstraZeneca over production delays and the company's failure to deliver on the number of jabs agreed.
Speaking at the Monkey Puzzle Day Nursery in Greenford, the PM was quizzed on whether his roadmap should be sped up, as Tory lockdown sceptics have demanded.
"The libertarian in me is also trying to protect people's fundamental right to life and their ability to live their lives normally," Mr Johnson said.
"The only way to restore that for everybody is for us to beat the disease and the best path to freedom is down the cautious but irreversible roadmap that we've set out."
The PM refused to confirm whether vaccine passports would be a part of all restrictions easing, despite suggesting on Wednesday that proof of vaccination could be required to get access into venues in the future.
Mr Johnson did say "certification will play a role" but said details were still being discussed.
ITV News Political Correspondent Shehab Khan has more on vaccine passports:
Speaking in the Commons on Thursday, the health secretary said he "couldn't answer" whether the Coronavirus Act - which allows the government powers to enforce lockdown measures - would continue beyond the next six months.
Opening the debate on coronavirus regulations, Matt Hancock said: "I cannot answer whether we will be retiring it in six months. My preference would be yes, but given the last year, I think a prediction would be hasty."
In a move to appeal to the lockdown-sceptics in his party, Mr Hancock told MPs the Act would only be retained "as long as they are necessary".
PM pledges to 'keep working with EU' on vaccine supply issue
On the issue of vaccine supplies, the PM said on Thursday his government would "keep working with our EU partners, and our friends."
A joint statement issued earlier this week said the two sides were seeking a “win-win” deal to increase supplies across the UK and EU.
It prompted reports Mr Johnson could be preparing to offer jabs, intended for the UK, to the EU.
ITV News Europe Editor explains the latest in the discussions around vaccine supply:
Speaking on Thursday, the PM said: "This is an international venture, the creation of vaccines is international. We're going to get on with our programme.
He added: "But the one thing I would say is that we're on the side of openness. One thing I'm firmly libertarian about is free trade and I don't want to see blockades of vaccines or of medicines, I don't think that's the way forward, either for us or for any of our friends."
The Calling Peston podcast explores if the UK's vaccine rollout is still on track: