Hancock said there had been a “very significant” impact from the delta variant of Covid first detected in India over the last month, which is now the dominant strain in England, according to official estimates.
He pointed to a renewed rise in Covid cases but said he had been reassured by a broadly flat rate of hospitalisations and deaths as officials consider plans to end the lockdown.
“It’s too early to make a final decision on that,” Mr Hancock told Sky News.
“The prime minister and I and the team will be looking at all the data over this week. We’ve said that we’ll give people enough time ahead of the June 21st date.
“We are not saying ‘No’ to June 21st at this point,” he added.
Mr Hancock said it was important that people receive both doses of Covid vaccines as the data showed this could protect effectively against the delta variant.
Britain’s swift vaccine rollout had weakened, but not broken, the link between the virus, hospitalisation and death, Mr Hancock said.
Last week, British prime minister Boris Johnson said he could see nothing in the data that would derail the plan to end lockdown restrictions, although caution was needed.
Britain’s overall death toll from the pandemic stands at 127,836 and is the sixth-highest in the world, according to Johns Hopkins University data.