According to UK government estimations, the delta version of Covid-19, which was first found in India last month and is now the dominant strain in England, has had a "quite significant" impact, according to Hancock.
He noted a resurgence of Covid-19 instances, but said he was comforted by a relatively flat rate of hospitalizations and deaths as officials explore ways to lift the lockdown.
"It's too early to make a final decision on that," 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 21 date.
"We are not saying 'No' to June 21 at this point," he added. Hancock said it was important that people receive both doses of Covid-19 vaccines as the data showed this could protect effectively against the delta variant.