The business secretary says it is necessary to be "measured and cautious" because of the Indian COVID-19 variant but it is "very likely" all restrictions will be scrapped by 21 June.
Kwasi Kwarteng defended the decision to ease the lockdown amid fears the variant, also called B.1.617, could derail England’s final roadmap step.
His comments comes as people across England, from today, are again able to enjoy hugs with loved ones, indoor pints and foreign holidays but as Boris Johnson also urged a "heavy dose of caution" due to the threat of the Indian variant.
There have so far been more than 1,300 cases of the Indian variant found in the UK, and Health Secretary Matt Hancock on Sunday warned it is "becoming the dominant strain" in places such as Bolton, as well as Blackburn.
Mr Kwarteng told Sky News: "Yes, things are opening up but people should have common sense, they should use judgment and I think if we act in a reasonable way, there is no reason to suppose that we can’t reopen the economy entirely on June 21.
"I think there has to be a degree of common sense, a bit of caution and people shouldn’t be running away being too exuberant, I suppose.
"I think we just need to be measured and cautious."
Asked whether the unlocking next month could still happen despite a growing number of Indian variant cases, Mr Kwarteng said that he "fully" expected the 21 June date would be met, adding: "I think it is very likely to happen."
He added: "I’ve said the vaccines are working against the Indian variant, I think we’ve got to look at the numbers so we’ve got some flexibility but there is nothing I have seen and nothing the Prime Minister has seen up to now that suggests we are going to delay that June 21 date."
As the country moves to stage three of the prime minister‘s roadmap for lifting lockdown restrictions, friends and family will enjoy greater freedom to gather together.
This includes being able to meet outdoors in groups of up to 30 and gathering indoors in groups of up to six, or as two households.
Pubs and restaurants are also once again able to serve customers indoors, while cinemas can reopen, fans can return to sports stadiums, and the ban on foreign holidays is lifted with people allowed to travel to a limited number of countries on the "green" list.
In addition, the government is now allowing people to choose whether to socially distance with family and friends when they meet up – although ministers have urged people to think carefully about the risks of hugging.
Health Secretary Matt Hancock has not ruled out imposing local lockdown restrictions in places worst affected by the Indian variant of coronavirus.
In Bolton, where a number of people have ended up in hospitals with the Indian variant, the "vast majority" of those patients had been eligible for a COVID jab but not yet had one, Mr Hancock said.
On Sunday, large queues were seen in Bolton after health authorities there invited any adults to attend for a vaccine in order to help combat the spread of the variant.
Mr Kwarteng reiterated the need for caution in the roll out of the vaccine to all age groups, saying guidelines were in place for a reason.
Referring to Bolton, he told Sky News: "I can see what they are trying to do, I can see exactly what they are trying to do.
"But what I’ve said is that there is a really good way that we’ve managed to roll out the vaccine and we would urge people to follow the guidelines that we’ve set out and the method that we’ve used."