Johnson said the government would accelerate remaining second doses to the over 50s and those clinically vulnerable to just eight weeks after the first dose and would prioritise first doses for those eligible who had not yet come forward.
Even so, the spread of the variant could disrupt Britain's progress out of lockdown, making it more difficult to move to the final stage of a staggered reopening of the economy in June, he said.
Johnson had aimed to lift all restrictions on June 21, after allowing people in England from Monday to hug again, meet in small groups indoors and travel abroad.
The United Kingdom has delivered one of the world's fastest inoculation campaigns, giving the first shot to almost 70% of the adult population and a second to 36%, helping to reduce infection rates and deaths.
But the emergence of the B.1.617.2 variant in parts of northern England and London has prompted some scientists to call for the reopening to be delayed, and a rethink on the speed of the vaccine rollout.
At the national level, infections are still low, and fell for a fifth consecutive week in England, Office for National Statistics (ONS) figures showed on Friday.