Speaking on Sky News on Sunday, the health secretary confirmed that the new strain is 40 per cent more transmissible than the Kent variant.
The Indian variant, now the dominant strain in the UK, has been spreading fast in the north-east.
On Saturday, official figures showed that Covid cases were up 70 per cent in a week.
Friday saw the highest number of new cases since March, with 6,238 transmissions recorded in 24 hours.
Government scientist Professor Stephen Reicher has said it would be “foolish” to push ahead with reopening on June 21 while cases were growing.
Speaking to Sky News on Sunday morning the Health Secretary said the virus was “more difficult to manage” with the new variant.
“But crucially, after two doses of vaccine we are confident that you get the same protection that you did with the old variant,” he said.
“So the good news is that the vaccine still works just as effectively.
“Everybody must go and get their second jab though because the first isn’t as effective on its own.
“So ultimately it does make the calculation more difficult for June 21 but it doesn’t change our strategy which is we all need to go and get vaccinated and that way we will break this link between the number of cases to the number of hospitalisations.”
All restrictions were due to be lifted on June 21 under Boris Johnson’s road map out of lockdown.
However, the government has always insisted that they will be driven by “data not dates”, leading to speculation that the date will be pushed back.
Correspondent Richard Pallot said: “Government sources have again stressed that no decision has been made but I understand that in private other plans are being drawn up.
“If there was a two-week delay then in theory all over 50s would get a chance of a second vaccine.”
Chris Hopson, the chief executive of NHS Providers, has said that the Covid-19 vaccine had appeared to have “broken the chain” between catching coronavirus and becoming seriously ill.
He told BBC Breakfast on Saturday that the number of people in hospital with the Indian variant was not increasing “very significantly”.
He said many of those in hospital in Bolton – which has the highest number of cases of the Indian variant in England – were younger than in previous waves of the pandemic.
It is understood there are GPs in Bolton who have begun offering vaccines at a 28-day gap, in the face of pressure not to waste any doses.
Some patients are believed to have been contacted by text message to say they are eligible for a second jab after four weeks, rather than the eight to 12 week gap advised by the Joint Committee on Vaccination and Immunisation (JCVI).
Comments on the NHS Bolton Clinical Commissioning Group (CCG) Facebook page indicate 16 and 17-year-olds are being offered a vaccine.