The scale of Tory anger with Theresa May for seeking a delay to Brexit has been laid bare after most of her MPs, including four cabinet ministers, refused to back any request for an extension to article 50.

Almost 100 Tory MPs voted against the prime minister’s decision to ask for a three-month extension to article 50 and another 80 abstained, underlining the loss of control over her party. Andrea Leadsom, Chris Grayling, Geoffrey Cox and Liam Fox all did not vote on the motion to extend article 50 until 30 June.

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May only won the vote on the back of support from Labour and other opposition parties, with only 31% of her backing coming from 131 Conservative MPs.

Pro-Brexit MPs suggested this showed she may not have the backing of her party to pursue any soft Brexit deal involving a customs union and ultimately no overall parliamentary majority for that if at least 100 Labour and other opposition MPs insist on a confirmatory referendum.

Play Video 0:34 MPs approve May's article 50 extension – video

Marcus Fysh, a Eurosceptic Conservative, said: “Only 133 out of 314 Conservative MPs voted for extension of article 50 this afternoon. The government simply does not have support for its current direction on the main purpose of its existence, inside the parliamentary party, the party in the country, or the wider country.”

May will go ahead anyway with her request for a delay until 30 June at an emergency summit on Wednesday evening, but EU leaders are planning to force her to accept a longer extension to article 50 of up to a year.

Conservative anger at any further delay suggests May will receive a difficult reception when she returns from Brussels to give a statement in the Commons on Thursday.

Brexiter cabinet ministers are not expected to resign at this point, as they fear being replaced by pro-remain ministers at a crucial time. However, some are questioning how long May can realistically continue as prime minister having previously promised not to endure a delay to Brexit longer than 30 June and without the support of most of her party.

One cabinet source said May’s government, now pursuing talks with Labour, was increasingly becoming divorced from the cabinet and the rest of the party, calling the prime minister’s future into question.

A tipping point for cabinet resignations is more likely to be if May were to reach a deal with Labour on a softer Brexit involving a customs union. Fox, the international trade secretary, hinted he could not put up with that outcome in a letter to the 1922 Committee of Tory backbench MPs, describing a customs union as “the worst of all worlds”.

Some Eurosceptics are also warning European leaders that they face non-cooperation from the UK if they proceed with a long delay.

In the Commons, Tim Loughton, a former minister, said: “If the EU elections go ahead, it is highly likely that UK will elect an army of Nigel Farage mini-mes who will frankly wreak havoc with the European parliament and wreck your calculations about the balance of power within the EU.”

Jacob Rees-Mogg, the leader of the European Research Group (ERG) of pro-Brexit MPs, also warned the EU that it could not count on cooperation from any future prime minister. “Parliament cannot bind its successors, the prime minister’s promises have not invariably proved reliable and there has been little sincerity from the EU,” he said.

Anger also bubbled over at a meeting of the Bruges Group thinktank, with audience members shouting “fuck government” and repeatedly yelling “traitor!” at the mention of May.

Mark Francois, the vice-chairman of the ERG, said people in the UK could not be “held captive against their will”.

Francois warned the EU that trying to keep the UK in the bloc for longer would create “perfidious Albion on speed” and a “Trojan horse within the EU, which will utterly derail all your attempts to pursue a more federal project.”

He added: “A new Conservative government led by someone like Boris or Dominic Raab might well vote down your projects, veto your attempts at greater military integration and generally make it impossible for you to bring about the more federal project in which you so desperately believe.”

Another Conservative MP, Andrew Bridgen, said the UK’s EU membership had turned the country from a Michelin-starred restaurant to one reliant on microwave meals.

He said: “We used to create these fantastic dishes from scratch and over the years this has been corrupted and we have been deskilled.

“Now we accept our laws pre-packed from Brussels, ready to go in the microwave. We’ve become a chicken ding parliament with chicken ding politicians.”

As well as dealing with splits over Brexit, the Conservative party is facing a crisis over recruitment, with the average age at which more people support the party than Labour rising from 47 to 51 since the 2017 election.

At an event on Tuesday to launch a thinktank report into the issue, the health secretary, Matt Hancock, warned that voting Tory “used to be something people started to think about doing when they got their first paycheck – now it’s when they get their first winter fuel allowance”.