Boris Johnson has urged people to act “with a heavy dose of caution”, as pubs and restaurants reopen indoors across England on Monday against the backdrop of a rise in cases of the Covid-19 variant first detected in India.

The call came after Matt Hancock, UK health secretary, on Sunday reinforced warnings by the prime minister at the end of last week that there was “a risk” the emerging variant could knock off track plans to scrap the last coronavirus restrictions in England on social contact on June 21.

Hancock refused to rule out the possibility of reversing the easing of restrictions on Monday — the third stage of the lifting of the lockdown imposed in January — but added: “That is not we are looking to do.”

Johnson said the conditions were right to reopen the hospitality and leisure sectors but called on everyone to play their part to keep the virus in check.

“We are keeping the spread of the variant first identified in India under close observation and taking swift action where infection rates are rising,” the prime minister said.

“But now everyone must play their part — by getting tested twice a week, coming forward for your vaccine when called and remembering hands, face, space and fresh air.”

From Monday, people can meet outdoors in groups of up to 30 and six people or two households can meet indoors. Museums, cinemas, theatres and sports stadiums can also reopen, albeit with restrictions in place, while foreign travel can resume.

Hancock said there was increasing confidence that vaccines worked against the emerging variant first detected in India and designated B.1.617, but warned that it could “spread like wildfire” among the unvaccinated. He said there was “a high degree of confidence it transmits faster” than the dominant variant in the UK, which was first detected in Kent.

The NHS was deploying a surge vaccination programme to hotspots, notably in Bolton, where there has been an uptick in cases of the variant. A new vaccination centre will open in the town on Monday.

Hancock told the BBC’s Andrew Marr programme that, of 18 hospital admissions in Bolton, “the majority” of cases involved people “who haven’t had the jab but are eligible for the jab”. He said five of those had received a single jab while only one patient, who was frail, had received two doses.

Hancock urged everyone who was eligible for a vaccination — but had not taken it up — to come forward. He also said that over-35s would be invited to have a jab this week.

He rejected criticism by the Labour party that the government acted too slowly in putting India on the red list for Covid-19, requiring new arrivals to quarantine in government-approved hotels.

Pakistan and Bangladesh were put on the red list on April 9 but India was not added until April 23. Labour has claimed Johnson was reluctant to upset Indian prime minister Narendra Modi, with whom he was trying to strike a trade deal.

Hancock insisted that more arrivals from Bangladesh and Pakistan tested in the UK ahead of April 9 were positive for Covid-19 than those arriving from India.

“They should have put India on the red list at the same time as Pakistan and Bangladesh,” said Yvette Cooper, the Labour chair of parliament’s home affairs select committee.

“Since then, we’ve had this three-week period in which thousands of people have returned from India — and that probably includes hundreds of the new variant Covid cases.”

John Edmunds, epidemiologist at the London School of Hygiene and Tropical Medicine, told the BBC that the B.1.617 variant was likely “to become dominant soon”.

He said that if India had been added to the red list earlier, it “could have delayed things a little bit” but he thought the arrival of the new strain could not have been avoided.