Health minister Matt Hancock on Sunday told Sky News that England will make a final decision on the last phases of the economy reopening on the 14 June.
The news comes ahead of the next phase of re-openings on Monday and amid increased jitters from public health officials and scientists about the spread of the the B.1.617.2 Indian variant, which has been found to spread more rapidly.
Prime minister Boris Johnson said in a press conference on Friday that the variant could pose a "serious disruption" to life returning to some normality in England on 21 June.
Cases of the variant almost tripled to 1,313 in the past week in England.
The next stage of easing taking place on Monday will allow people to hug each other and allow for indoor dining and drinking in hospitality venues.
Museums, cinemas, theatres and sports stadiums can also reopen, and indoor exercises resume.
People will also be able to travel abroad to "green list" countries without needing to quarantine when they return.
Disruption to the roadmap could cause headaches for these businesses which have already weathered a difficult year.
"We'll make a final decision for step four, which is the biggest step on the roadmap. We'll make that final decision on the 14th of June," Hancock said, adding that early data showed that vaccines are effective against the variant.
The government has been accused of not shutting its borders to India quickly enough as caseloads escalated there.
By the time a travel ban from India had come into force caseloads had topped 330,000.
Surge testing is in force to keep the variant at bay in England, but despite this, medical officials have expressed serious concern about allowing hospitality to reopen indoors.
Watch: COVID-19: Health Secretary Matt Hancock warns Indian variant can 'spread like wildfire' among those not vaccinated