MPs have backed Covid passes being required at nightclubs and large venues across England, as dozens of Tories rebelled against the government’s “plan B” winter Covid measures to tackle the spread of the Omicron variant.

The prime minister made a last-ditch call for his backbenchers to support the move in a private meeting an hour before the first vote, and managed to win over a few.

However many still said they would oppose the move, branding the new rules illiberal, a “fundamental change in the relationship between the citizen and state” and a “knee-jerk” reaction.

The requirement for people to show a Covid pass – proving their vaccination status or a recent negative test result – will come into force from Wednesday. It was passed by 369 votes to 126.

Labour said that 101 Conservatives voted against the government, by far the largest rebellion of Johnson’s premiership since the 2019 election.

Earlier, MPs endorsed the need for masks to be worn in shops and on public transport by 441 votes to 41.

During a debate in the Commons on Tuesday, Tory MPs raised concerns over the recent problems some people have reported in ordering lateral flow tests, saying this would hinder some people’s ability to use a Covid pass to access some venues.

Some backbenchers also claimed that forcing people to confirm their vaccine status was unethical, and there was no evidence it would avoid them passing Covid on because even those who have been vaccinated could catch and transmit the virus.

Andrea Leadsom, a former cabinet minister, said the new Covid rules would “continue to hurt our constituents” and his out at “creeping regulation”. She said it was unthinkable MPs would be limiting the quality of life for all citizens “just to be on the safe side”, and vowed to vote against the “illiberal rules”, adding it was “truly appalling” to justify them by saying they were less authoritarian than other countries’.

Tim Loughton, another former minister, also said: “We cannot head for the hills with knee-jerk emergency measures every time a new variant comes along.”

New Tory MP Miriam Cates claimed there had been “permanent change to the understanding of what liberty is”. Another, Anthony Mangnall, urged: “We cannot continue to terrify people.”

Richard Drax, a veteran backbencher, accused the government of hitting hospitality businesses by “instilling the fear of god into their customers”.

The health secretary, Sajid Javid, said the measure did not amount to a “vaccine passport”, saying it was “really important to me as a point of principle that people have a range of different routes to show that they are eligible”.

He said there had been a rapid increase of Omicron cases and recent data had proved more cause for concern because the increased transmissibility of the variant meant it still had the potential to overwhelm the NHS.

During the debate, Tory MPs repeatedly pressed Javid over their concerns more restrictions could be imposed after the Commons breaks for recess on Thursday.

The former cabinet minister Chris Grayling said he was concerned to hear ministers were considering a “plan C” for tackling Covid, and Mark Harper, a former chief whip who now chairs the Covid Recovery Group, said MPs should be recalled to sign off any new restrictions imposed once recess begins.

Labour said it would back the government in all the votes, on face coverings, Covid passports, and requiring NHS staff to be vaccinated.

Wes Streeting, the shadow health secretary, said: “No matter how dysfunctional the Conservative party has become, the country can rely on Labour.

“We will act in the national interest as we have done throughout the pandemic, putting public health before party politics, by supporting the motions under consideration this afternoon.”

Streeting said masks “are simply a price worth paying for our freedom to go out and live our lives during this pandemic”, and urged people to limit their interactions at work, take a test before attending large indoor social gatherings, and get their booster jab.