Dame Anne Johnson, the president of the Academy of Medical Sciences, said next week will be "absolutely critical" in looking at data on infections.
Concerns are mounting over whether the emergence of the Delta variant threatens the government's provisional June 21 deadline for lifting virus restrictions. Only the headline has been changed.
The comments come as Covid-19 cases have continued to surge in the United Kingdom amid reports Boris Johnson is considering delaying so-called freedom day by at least two weeks in order to allow more people to be fully vaccinated against the Indian variant.More news: Pope voices sorrow over Canadian deaths, doesn't apologize
Hancock said there had been a "very significant" impact from the delta variant of COVID-19 first detected in India over the last month, which is now the dominant strain in England, according to official estimates. "And separately we have a piece of work on what the social distancing rules should be after that", he said.
"It's too early to make a final decision on that", he said, adding that the government was still considering the date of June 21 at this point.
Mr Hancock told Sky News' Trevor Phillips On Sunday programme that vaccines had "severed but not broken" the link between a rise in cases and an increase in the number of people being admitted to hospital.
Former prime minister and Labour leader Tony Blair has argued that those who have been given both shots should be afforded extra freedoms as an incentive for people to take up the inoculation offer.More news: Biden Declares US Will Donate 80 Million Vaccine Doses
"The tireless efforts of NHS staff to protect the people they care for and their communities has quite simply saved lives, and when you get the text, you're next".
Mr Hancock told MPs: "From this week we will start offering vaccinations to people under-30, bringing us ever closer to the goal of offering a vaccine to all adults in the United Kingdom by the end of next month".
It comes as a surge in Covid-19 cases including the Indian variant continues to spread across the UK.
A further four deaths have also been recorded within 28 days of a positive COVID test - that's down from 13 on Saturday and six last Sunday.More news: Teen Shoves Bear off Wall To Save Her Dogs in Viral Video