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.
The Health Secretary, pressed on whether the June 21 removal of restrictions could be postponed if the Indian variant data "gets bad", told the BBC's Andrew Marr Show: "We are absolutely open to doing that if that's what needs to happen".
- The Delta variant of the coronavirus, first discovered in India, is estimated to be 40 percent more transmissible than the Alpha variant that caused the last wave of infections in the UK, Britain's health minister said Sunday.
"This week we will be opening up vaccines to the under-30s and so we are getting a step closer to the point when we have been able to offer the vaccine to all adults in this country", he said. But people who have received two doses of vaccine, should be equally protected against either variant, he added. One of the four critical tests set by the government for a reopening is that the assessment of the risk from the deadly virus is not fundamentally changed by new VOC.
"We just don't know the potential for that to be (a) vaccine-defeating mutation and simply don't want to take the risk as we come up to June 21", UK Transportation Secretary Grant Shapps said.
"So ultimately it does make the calculation more hard for June 21 but it doesn't change our strategy which is we all need to go and get vaccinated and that way we will break this link between the number of cases to the number of hospitalisations".
He also suggested social distancing, wearing of face masks and working from home could be extended beyond the final stage of the government's "road map".
"The way we are looking at this is step four [of the roadmap] involves the removing of the remaining social restrictions like the rule of six and some of the business closures which are still there".
More than 40 million people across the United Kingdom have so far had a first dose of a vaccine. A mass vaccination campaign that started in December has given two doses of vaccine to more than half the adult population and brought new infections and deaths down sharply.
On Friday the United Kingdom recorded its highest number of new confirmed coronavirus cases - 6,238 - since late March, according to official figures, although Saturday's number was down slightly at 5,765 lab-confirmed cases.