He sounded the alarm as Boris Johnson admitted the new strain of the disease could make it more difficult to move to the last stage of easing lockdown in June.
In response the prime minister announced plans to slash the amount of time the over-50s and the clinically vulnerable have to wait for their second dose of a Covid-19 vaccine, from 12 weeks to 8.
But he rejected calls from local leaders to vaccinate all young adults in virus hotspots.
And there was no need to delay the road map reopening set for Monday, which will see people able to socialise indoors, he said.
But the June 21 date is now in jeopardy, he suggested.
And he warned that if the new variant turned out to be much more transmissible than other strains, the country could face "hard choices" ahead.
Scientific advice released as Mr Johnson was speaking said it was a “realistic possibility” that the Indian variant is as much as 50 per cent more transmissible than the Kent variant, which spread rapidly across the UK this winter.
If this growth advantage translates to sustained wider transmission on a regional or national basis, this could lead to a “substantial resurgence” in hospitalisations that place “unsustainable pressure” on the NHS, according to documents published by the Scientific Advisory Group for Emergencies (Sage). The group added that the lifting of restrictions on Monday risked a significant Covid surge.
Professor Chris Whitty told a Downing Street press conference: "We expect over time this variant will overtake and come to dominate in the UK" in the same way the Kent strain did.
The variant has been found in at least 15 areas of England, where councils and Public Health England (PHE) officials are working to contain any clusters.
Prof Whitty said the strain was “quite widely seeded in a number of parts of England and indeed elsewhere in parts of the four nations of the United Kingdom”.
Coronavirus rates in Bolton, which had been going down, have been going up “very significantly over the last couple of weeks”, he added.
Rates have not been rising in the over-60s, however, the group more likely to need hospital treatment, become severely ill or die.
He added that “this may be a delay or the vaccine is helping to protect those who are older and who are vaccinated”.
He added: “(The) vaccine deployment programme remains successful, vaccines are reducing hospitalisations and deaths - there is very clear evidence they are and nothing has changed on that.
“Infection rates are not causing NHS pressure - the data on that is really clear, and with the variants of concern, excluding the (India variant), really there’s no change - most of them are relatively stable.”
While scientists believe that vaccination will protect against severe disease and hospital admissions from the variant, “we’re not so confident about the degree to which it protects against milder disease and transmission, and that’s just because we don’t have the data but that will come with time,” he said.
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