Those aged over 50 and those considered clinically vulnerable will be able to get a second vaccine dose after eight weeks, the prime minister has announced.
Boris Johnson said plans to accelerate vaccinations for priority groups would not affect the scheduled easing of lockdown in England from Monday.
But the prime minister said Indian coronavirus variant could cause "serious disruption" to the next stage of lockdown easing on 21 June.
However, he did say there was "no evidence" to suggest the vaccines currently in use would be less effective against the B.1.617.2 strain.
Professor Chris Whitty, the chief medical officer for England, has confirmed that the strain first identified in India is "more transmissible" than the variant first found in Kent, according to modelling.
He added: "Now, the question in practical terms, over the next two to three weeks, is ‘Is this somewhat more transmissible? than [the Kent variant], or is this a lot more transmissible?’
"And that will have implications for the long term prospects of this epidemic."
It comes as four people in the UK died with the Indian variant of COVID-19 – the first known domestic deaths from the new variant of the virus.
The four deaths from the strain of the virus, now designated a "variant of concern", took place between 5 May and 12 May.
There is evidence that the Indian variant could spread at least as quickly as the UK variant first discovered in Kent, which fuelled England’s second wave of infections, according to Public Health England (PHE).
It said on Thursday there had been 1,313 cases in England of the Indian variant in a week, more than double the previous week’s figure, along with the four confirmed deaths.
Britain put India on a travel "red list" in April, meaning all arrivals from India – now in the throes of the world’s worst wave of coronavirus – would have to pay to quarantine in a government-approved hotel for 10 days.
The variant is thought to be spreading in certain areas of the UK, including Bolton and Blackburn, but since overall case numbers remain low, broader risk levels remain lower than they were for much of the winter.
Early evidence also provides tentative signs the new variant is not resistant to the vaccines.