The "last thing in the world" the government wants is another lockdown, Culture Secretary Oliver Dowden has said, adding it is on track with the lockdown easing plan.
He said dates "could be delayed if the situation deteriorates" but ministers were confident in the "cautious path".
It comes as the head of NHS England urged people not to "squander the gains" made in recent months.
On Monday in England, two households or groups of up to six can meet outside.
The "stay at home" guidance will also be lifted, outdoor sports facilities will reopen and small weddings can take place. The next stage - due no earlier than 12 April - will allow non-essential retail, restaurants and pubs to reopen.
In Wales, the "stay local" rule was lifted on Saturday and six people were allowed to meet outside.
Mr Dowden was asked on BBC One's Andrew Marr Show whether he could guarantee that this would be the last lockdown.
"Well, this is why we've chosen to go on this cautious path," he said. "The aim of doing this is to make sure that it's irreversible."
Mr Dowden said the dates "could be delayed if the situation deteriorates but at the moment we're on track".
He told the programme: "My whole experience of the past year, and I think everyone that's watching's experience of the past year, is you can't rule things out.
"But we have every confidence we won't have to have another lockdown because we've done this and it's the last thing in the world we would want to do."
On Saturday, Mr Johnson also said the roadmap was still on course, and nothing in the data dissuaded him from the plan.
The return of the legal right in England to go for a walk in the rain with five other people feels like quite a big moment.
And that reminds us of something: alongside the health emergency, the hundreds of thousands of grieving relatives and an economic crisis, this is the ongoing era of liberties crushed for everyone, the world and life shrunken and greyer than before.
That's why the government is so desperate to avoid the psychological whiplash of yet another slamming on of the brakes, or a reversal.
That's why there's the constant refrain of the roadmap, as they call it, being cautious but irreversible.
And that's why, despite the prime minister's instinct to inject his language with optimism, there's been a concerted effort in recent months to manage our expectations, to minimise the miles between our realistic hopes and potential reality.
For this pandemic has cruelly taught us, repeatedly, that the road back to normality will contain hairpin bends we haven't yet seen.
And for every fleeting moment of feeling like we are getting there - and everyone hopes we are - it's still another fortnight, at least, in England, before it's legal to go to the hairdressers.
The abnormal has become normal, but it's worth reminding ourselves just how remarkable it still is.
But even after lockdown, there will still be the need for social distancing, testing and self-isolating of a while to come, suggested Prof Mark Woolhouse, who sits on a group that feeds into the government's Scientific Advisory Group for Emergencies (Sage).
"I still suspect that looking forward, and I am talking now right through 2021 and into the years ahead, that we are still going to have to be alert to coronavirus," he said.
"There are still going to be situations where we might need to use personal protective equipment, we might well need to do some kind of social distancing, put some kind of biosecurity measures in place."
He said a lot of workplaces, retail and hospitality "can be made safer" and for places like nightclubs or large concerts, "that's where passports come in - whether it is vaccine passports, test-negative passports or even immunity passports".
But the chairman of the scientific body the Royal Institution, Sir Richard Sykes, said the UK has "gone from being cavalier to crippling caution" when it comes to handling Covid.
"If we are not now well-prepared to put up with anything that's thrown at us, then it's God help all of us because that's the best we can do at this point in time," he told BBC Radio 4's Broadcasting House programme.
'Not job done'
It comes as Prof Stephen Powis, NHS England national medical director, warned that coronavirus could still "wreak more havoc and ill-health on a significant scale" and cited concerns over variants.
Writing in the Sunday Telegraph, he said the prospects "look immeasurably brighter and more positive" but said that the easing "does not mean job done".
Prof Powis said: "We've made enormous progress that we need to build on and not squander the gains we've made."
He added: "We need to hold our nerve and drive for the line, so everyone can get back safely and soon to our normal lives."
While there are thousands of different versions, or variants, of Covid-19 circulating, those that are of particular concern were first detected in the UK, South Africa and Brazil.
Several European countries are already battling a third wave of coronavirus infections - the effects of which Mr Johnson said will "wash up on our shores".
There also remain ongoing tensions over vaccine exports on the continent.
However, the prime minister has insisted that there is "absolutely nothing in the data" to discourage him from easing restrictions as planned on Monday.
How are rules changing on 29 March in England?
- People will be allowed to meet outside - including in private gardens - in groups of up to six, or as two households (with social distancing)
- The stay-at-home guidance is ending, although the government is urging people to stay local as much as possible; holidays away from home are still not allowed
- Outdoor sport facilities will reopen, including golf courses, tennis and basketball courts, and outdoor swimming areas
- Formally organised outdoor sports can restart
- Weddings can take place, attended by up to six people
Wales became the first UK nation on Saturday to lift travel restrictions within its borders, allowing unlimited travel within the country.
Scotland's stay-at-home rules become "stay local" on Good Friday and Northern Ireland's stay-at-home message is to be relaxed on 12 April.
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