Surge vaccinations have not been ruled out as a way to deal with the rise of the Indian variant, No 10 has said.
On a visit to Durham, Prime Minister Boris Johnson said he was "anxious" about the variant and did not rule out reintroducing regional restrictions.
But he said there was no evidence to suggest England's planned lockdown easing could not go ahead.
Covid jabs are already being opened to all over-18s in parts of Lancashire to tackle the Indian variant.
The government's scientific advisers, known as the Scientific Advisory Group for Emergencies (Sage), are meeting later to discuss the spread of the Indian variant.
The India variant - officially called B.1.617.2 - is
one of four mutated versions of coronavirus which have been designated as being "of concern" by UK public health bodies, with others first being identified in Kent, South Africa and Brazil.
Experts believe the Indian variant has mutations that may make it more transmissible, but it is not yet known if it causes more severe disease or if it might make current vaccines less effective.
Speaking at a primary school in Ferryhill, County Durham, Mr Johnson said: "It is a variant of concern, we are anxious about it.
"At the moment there is a very wide range of scientific opinion about what could happen.
"We want to make sure we take all the prudential, cautious steps now that we could take, so there are meetings going on today to consider exactly what we need to do.
"There is a range of things we could do, we are ruling nothing out."
The surge vaccination plan would mean focusing extra doses of the Covid-19 vaccine in specific areas to immunise a larger section of the population, and reduce the spread of variants.
Extra doses of the vaccines have been given to Blackburn and Darwen in Lancashire in order to
open up jab appointments to all over-18s in the area.
The younger age groups will be offered the vaccine from next week, when surge testing will also take place, Blackburn and Darwen Council said.
But sources told the BBC that surge testing in areas where the variant has been found "isn't working".
The current strategy was identifying cases but not stopping the spread, they told the BBC.
The sources added that cases of the variant were being seen in many places with no links to travel and case numbers have been "grossly underestimated".
The BBC's senior political reporter Matt Cole said sources told him that while England was still expected to move to stage three of the roadmap out of lockdown on 17 May and the PM is thought to have signed off some reduction in social distancing measures. a politically difficult rethink may now be under consideration.
Questions are also being raised about the potential need to delay stage four, due on 21 June, when the government hoped to remove all legal limits on social contact.
One of the four key tests for ending coronavirus restrictions rests on the Covid-19 risks not being fundamentally changed by new variants.