The Government has yet to decide whether to proceed with a further easing of lockdown restrictions in England on June 21.
Updates on plans for domestic coronavirus "passports", announcements on easing social distancing requirements and further guidance on weddings could be pushed back due to uncertainty over the Indian variant.
The spread of the highly transmissible variant has placed plans for the further easing of restrictions in jeopardy despite the lifting of some lockdown measures across Great Britain on Monday.
Despite the appearance of the B1617.2 variant in the UK, Cabinet minister Kwasi Kwarteng insisted England's road map remained on track for the June 21 easing of the remaining restrictions if people acted responsibly.
But Downing Street said the spread of the variant could push back plans to set out guidance ahead of that date.
Last week Boris Johnson promised "we'll be saying more later this month about exactly what the world will look like on June 21 and what role there could be - if any - for certification and social distancing".
He also told MPs that "we will before the end of this month, set out all the details about the marriage world post-June 21".
But Downing Street refused to commit to those timetables on Monday.
The Prime Minister's official spokesman said: "We need time to assess the latest data on this variant first identified in India so I'm not going to give a set time for doing that.
"We want to do everything possible to give people enough time to prepare."
Although ministers believe the vaccines will be effective against the highly transmissible Indian variant of concern, there are worries about the impact of its spread on those for whom the jabs do not provide protection or people who have not yet had a shot.
The Prime Minister urged people to treat the latest easing of restrictions with a "heavy dose of caution" while Mr Kwarteng warned against excessive drinking for those returning to bars.
