ITV News Health Editor Emily Morgan explains why the variant is worrying the government so much
Speaking during a Downing Street press conference, Mr Johnson said the variant could make it "more difficult" for England to move to step four of the government’s roadmap out of lockdown in June.
But the PM has said Monday's reopening can go ahead as planned, with indoor socialising set to be permitted once again.
Data following Monday's relaxation will be assessed before the next step is taken to determine whether the June 21 reopening should go ahead, or local action could be taken instead.
The prime minister said if the Indian variant proves to be "significantly more transmissible" than other strains then "we’re likely to face some hard choices".
The Scientific Advisory Group for emergencies (Sage) has said there is a “realistic possibility” the variant could be as much as “50% more transmissible” than the Kent strain.
The minutes of the meeting between the government’s scientific advisers on Thursday said that it is “highly likely that this variant is more transmissible than B.1.1.7 (high confidence), and it is a realistic possibility that it is as much as 50% more transmissible”.
Mr Johnson on Friday warned: "I have to level with you that this new variant could pose a serious disruption to our progress and could make it more difficult to move to step four in June."
Meanwhile England's Chief Medical Officer, Professor Chris Whitty, has warned the Indian variant could become the dominant variant in UK.
How the Indian Covid variant has spread in the UK
He said if the Indian variant proved to be more transmissible than other variants, the UK could see "a really significant surge" in Covid-19 cases.
"That's a really critical question to which we do not yet have the answer," he added.
"If you’re seeing loved ones, think really carefully about the risk to them, especially if they haven’t had that second dose or if it hasn’t yet had time to take full effect," Mr Johnson said.
But Mr Johnson said there is "no evidence to suggest that our vaccines will be less effective in protecting people against severe illness and hospitalisation".
Prof Whitty continued: "We expect over time this variant will overtake and come to dominate in the UK in the way that the Kent variant did."
Health Editor Emily Morgan on the precarious position the UK is now in as the Indian variant spreads
This means there will be eight weeks in between doses, rather than 12 weeks - as a surge of infections caused by the Indian Covid-19 variant continue to grow.
Cases of the new strain have more than doubled in a week (from 520 to 1,313), with Public Health England "rapidly" investigating.
Surge testing is currently taking place in 15 areas across England, including Bolton, Blackburn, London, Sefton and Nottingham.
In Bolton, which has one of the highest case rates of the variant in the country, mobile testing units have been deployed and door-to-door PCR Covid testing has been offered to 22,000 residents.
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There will also be an acceleration of the vaccine rollout there, including longer opening hours at vaccination centres.
Secondary school and college pupils in Bolton and Bury are being asked to keep face coverings in place until further notice.
The advice comes after the government confirmed it will remove the face mask requirement for pupils in England from Monday, when more indoor mixing is allowed when restrictions are lifted further.
Coronavirus - What you need to know