Health Secretary Matt Hancock has given the clearest sign yet June 21's so-called Freedom Day could be pushed back by rising coronavirus case numbers.
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".
Mr Hancock admitted in an interview with the BBC’s Andrew Marr Show the emergence of the variant that was first detected in India had made decisions on easing "more difficult".
Ministers are “absolutely open” to delaying the unlocking in England, he said.
He stressed that June 21 was a “not before” date and that it was only “pencilled in” as the next step out of lockdown.
The comments come as Covid-19 cases have continued to surge in the UK 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.
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.
“We said in the road map that June 21 is the date by which we would not take Step 4 before that date and that we would look at the data.
“That is exactly what we are doing, so the road map was set up in order to be able to take these sort of changes into account.”
Mr Hancock admitted the emergence of the Indian variant, which has become dominant in the UK, had made the “calculation” on whether to proceed with unlocking this month “more difficult” as he confirmed the latest scientific advice is that the mutation – also known as the Delta variant – is 40% more transmissible than the Kent strain.
The Health Secretary said he “wouldn’t rule out” measures such as wearing face coverings in public settings and working from home where possible continuing in the long term.
“The way we are looking at this is Step 4 involves the removal of the remaining social restrictions like the rule of six and some of the business closures which are still there,” he told the show.
“And separately we have a piece of work on what the social distancing rules should be after that.”
In a separate interview with Sky News’ Trevor Phillips On Sunday programme, Mr Hancock said the Government “haven’t yet set out the approach to social distancing after Step 4” and that plans were currently being worked up with scientific advisers about how to proceed safely.
Mr Hancock said he expected “around three fifths” of all adults to have been fully-vaccinated by June 21, with 52% currently double-jabbed, as indicators suggest vaccines are helping to cut the link between case rises and an increase in hospital admissions.
In Kent cases remain low and in two areas the Indian variant, known as Delta by the World Health Organisation, has not been detected for a month.
Cases rose 40% last week across the county, while almost half of adults are fully vaccinated and 75% have received one jab.
The latest data shows infection rates in Kent remain low and levels have actually fallen in five areas.