He added the Indian strain is "something we are increasingly concerned about in the UK".
Cases of the variant are growing at a rapid rate, already making up an estimated quarter of new cases.
Mr Johnson stressed the need for caution and vigilance as lockdown is eased, with the next step on May 17.
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He said "the end of the lockdown is not the end of the pandemic".
"The World Health Organisation has said that the pandemic has now reached its global peak and will last throughout this year," Mr Johnson told the Commons today.
"Our own scientific advisers judge that although more positive data is coming in and the outlook is improving, there could still be another resurgence in hospitalisations and deaths.
"We also face the persistent threat of new variants and should these prove highly transmissible and elude the protection of our vaccines, they would have the potential to cause even greater suffering than we endured in January."
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January was the worst stage of the UK’s outbreak, when daily deaths hit 1,820 and hospital occupancy 39,200.
Current evidence suggests that vaccines will work against severe disease at least to some degree, but this has not been studied intensely in real world populations.
It is based on the fact it has fewer “escape mutations” in its genetics which allow it to dodge antibodies in the blood.
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The European Medicines Agency said today that it was "monitoring very closely the data on the Indian variant".
But it said there was "promising evidence" that mRNA vaccines - the types those produced by Pfizer and Moderna - would be able to kill it.
Mr Johnson said even without the prospect of a deadly new variant which could escape vaccines, there was a "high likelihood" of a seasonal surge in coronavirus cases in the winter.
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A third wave has been estimated by a range of scientific models, but estimates did not suggest this would put pressure on the NHS.
Sage estimates made earlier this year suggested a third wave could have killed more than 100,000 Brits.
But revised estimates, published by Sage on Monday, now show a much smaller 9,000 deaths in the "worst-case scenario".
However, none of the models accounted for new variants that might emerge with the ability to dodge vaccines.