Matt Hancock has warned that the Indian Covid variant could "spread like wildfire" amongst the unvaccinated as he refused to rule out local lockdowns.
The Health Secretary said there was a "high degree of confidence" that the jab works against the new strain as he urged people to get the vaccine.
But he would not rule out taking tougher measures if necessary - and said no decision would be taken about lifting final restrictions until June 14.
Mr Hancock told Sky's Sophy Ridge on Sunday: "We'll make a final decision for the step four, which is the biggest step on the roadmap, we will make that final decision on June 14.
"We've always said we want this to be cautious. We really want it to be irreversible."
A new variants spiralling out of control is one of the Government's key tests for lifting lockdown, he said.
"Because of the speed of transmission of this one, it can really spread like wildfire amongst the unvaccinated groups, hence we need to get as many people vaccinated as possible," Mr Hancock said.
The "vast majority" of people hospitalised with Covid in Bolton, a hotspot for the new variant, had been eligible for the jab but not take it up, he said.
Mr Hancock said early data from Oxford University labs offered a degree of confidence that the jabs work against the new variant, but warned it was "clearly more transmissible".
He said: "That means that we can stay on course with our strategy of using the vaccine to deal with the pandemic and opening up carefully and cautiously but we do need to be really very vigilant to the spread of the disease.
"We have a high degree of confidence that the vaccine will overcome."
Lockdown relaxations will go ahead on Monday, allowing indoor mixing, reopening of pubs and restaurants indoors, and foreign travel.
But Mr Hancock did not rule out reversing the changes if the Indian variant proves to be very highly transmissible.
He said: "I very much hope not and our goal remains, our strategy remains, to take a cautious and irreversible approach to ensure that we're always looking at the data all the way through, and crucially to use the vaccine to get us out of this pandemic."
He also signalled that local lockdowns could be implemented if necessary but said the focus was on testing and boosting vaccinations in affected areas.
"Given though Bolton has been in some form of kind of a lockdown for a year, it's not a step we want to take but of course we might have to take it and we will if it's necessary to protect people," he said.
SAGE adviser Professor Sir Mark Walport, warned the UK faced a "perilous moment".
"We have a variant that shows good evidence of being more transmissible and possibly significantly more transmissible," he said.
"We're going to have to watch the numbers extremely closely. And the other thing that we do know is that this new variant from India is actually quite widely distributed across the country."
Sir Mark said he would be staying outdoors and avoiding indoor pub visits despite Monday's relaxation of lockdown restrictions.
He said: "If you haven't had a vaccine you really must have one actually. There's no good reasons for not.
"So that's the important thing. But then it is I think a question of people making judgments and you know my personal judgment is that I will do things outside as far as possible."
Asked if he would avoid indoor pub tables, he said: "For the moment, yes."
