But on a more positive note, he said there is a “high degree of confidence” that the current vaccines are effective against the variant.
Hancock urged those who are eligible for vaccination but have not yet booked an appointment to come forward to get their jab.
The Health Secretary described the current situation as “a race between the vaccination program and the virus”, with the new variant having “given the virus some extra legs in that race”.
“And so even with the protection that the vaccine gives you — the vaccine protection is very high but it is not absolute.”
Public Health England (PHE) said cases of the variant known as B1617.2 in Britain have more than doubled to 1,313, up from 520 cases recorded by PHE last week.
However, Hancock said Monday’s planned easing of lockdown would still go ahead.
A decision would be announced on June 14 as to whether the country would proceed to the final stage on June 21, when all legal limits on social contact are expected to be removed, according to Hancock.
“We need to be cautious, we need to be careful, we need to be vigilant and we’ve said — at each step,” he said.
From Monday, pubs, bars and restaurants in England will be permitted to open indoors, while indoor entertainment will also resume, including cinemas, museums and children’s play areas.
People in England will be allowed to meet outdoors in groups of up to 30 people, and meet indoors in groups of up to six or as two households.
Hotels, hostels and B&Bs can also reopen from Monday.
But UK health experts warned that the next stage of lockdown easing should be approached “with utmost caution”.
Richard Jarvis, co-chairman of the British Medical Association (BMA) public health medicine committee, said “key segments of the population” were still not vaccinated.
According to the latest official figures, more than 36.3 million people in Britain have been given the first jab of the coronavirus vaccine.
As of Monday morning, the UK’s overall COVID-19 caseload has spiked to 4,466,589, while the death toll stood at 127,941.