The prime minister said: "I do not believe that we need, on the present evidence, to delay our road map and we will proceed with our plan to move to step three in England from Monday.
"But 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."
He added that if the Indian variant proves to be "significantly more transmissible" than other strains "we're likely to face some hard choices".
But he said there is "no evidence to suggest that our vaccines will be less effective in protecting people against severe illness and hospitalisation".
Mr Johnson announced that Over-50s will be given their second vaccination after eight weeks instead of 12 due to concerns about the Indian variant.
The latest figures show the number of infections caused by B16172, which has been designated as a “variant of concern”, has nearly tripled in England over the past week.