Theresa May’s high-stakes Brexit strategy may have been accidentally revealed after her chief negotiator Olly Robbins was overheard in a Brussels bar saying MPs will be given a last-minute choice between her deal and a lengthy delay.

The prime minister has repeatedly insisted that the government intends to leave the EU as planned on 29 March, and urged MPs to “hold our nerve”, while she tries to renegotiate changes to the Irish backstop.

“So our work continues,” she told MPs on Tuesday. “Having secured an agreement with the European Union for further talks, we now need some time to complete that process. The talks are at a crucial stage. We now all need to hold our nerve to get the changes this house requires and deliver Brexit on time.”

But Robbins, the most senior civil servant involved in the Brexit process, was overheard by a reporter from ITV, holding a late-night conversation in which he appeared to suggest she would wait until March – and then give MPs the choice between backing her, or accepting a long extension to article 50.

According to the broadcaster, Robbins said the government had “got to make them believe that the week beginning end of March ... extension is possible, but if they don’t vote for the deal then the extension is a long one.”

The tactic appears to be aimed squarely at members of the backbench Tory European Research Group (ERG), who may fear Brexit could ultimately be cancelled altogether, if MPs accept a delay.

“The issue is whether Brussels is clear on the terms of extension,” Robbins was overheard saying. “In the end they will probably just give us an extension.”

On the backstop, Robbins appeared to confirm that the government’s initial plan was for the backstop, which effectively keeps the UK in a customs union, to form a temporary “bridge” to the long-term trading relationship.

“The big clash all along is the ‘safety net’,” Robbins said. “We agreed a bridge but it came out as a ‘safety net’.”

Former Department for Exiting the European Union (DExEU) minister Steve Baker played down the leak, saying “as a consummate civil servant, Mr Robbins is likely to be appalled by this story. Officials advise. Ministers decide. What matters ultimately is the policy of the prime minister and the cabinet.”

But another senior Brexiter said “the trouble with Mr Robbins is that he is a draughts player in a chess world”.

Robbins’ revealing remarks are likely to embolden those ministers who are increasingly anxious about the threat of a no-deal Brexit.

Several are privately signalling they are prepared to consider resigning in a fortnight’s time to ensure the success of cross-party efforts to force May’s hand, rather than allow her to continue gambling on a last-minute change of heart by Brexiter rebels.

A government spokesman said “we don’t propose to comment on alleged remarks from a private conversation. The government’s focus is on securing the improvements parliament needs to pass a deal so we leave the EU on 29 March”.

But Robbins’ overheard comments chimed with remarks from the leader of the House of Commons, Andrea Leadsom, who refused to deny on Tuesday morning that the Commons could be denied a “meaningful vote”, until after the next scheduled European council meeting, which is due to be held on 21 March.

“The prime minister is seeking to bring back the meaningful vote just as soon as possible,” Leadsom told BBC Radio 4’s Today programme. “So it is a negotiation. It’s not possible to predict the future.”

However, if she seeks to delay until March, May is likely to face a fierce backlash from MPs, including some junior ministers, who believe every day of uncertainty increases the risks to jobs and businesses.

One senior backbencher said there was “a palpable sense that the longer this drags on, the more the prime minister has to have a specific proposal that can win over the ERG, which seems unlikely, or cross-party support for a deal. If not, she’ll face mass resignations and another leadership crisis”.

Another senior Conservative said: “It’s an utter tragedy that no-deal is still on the table. Cowards in the cabinet sit there updating Instagram, pretending everything is okay while we go through this bullshit parade. They’re lying to the British public and history will damn them forever.”

Jeremy Corbyn accused May of playing for time and having no plan. “Our country is facing the biggest crisis in a generation, and yet this prime minister continues to recklessly run down the clock,” he said. But May, in turn, blamed Labour for increasing uncertainty by failing to support her deal.

Robbins’ reported comments emerged after May cleared the way for a nerve-shredding, last-minute vote for her deal, by announcing that the government would seek to exclude the Brexit deal from the usual 21-day process under which parliament approves international treaties.

MPs are due to vote on Thursday on a government motion, reaffirming their conditional acceptance of May’s deal, if she secures changes to the controversial backstop.

When the Valentine’s Day vote was first mooted, it was regarded as a fresh opportunity for MPs to rule out no deal.

But a cross-party group of MPs led by Labour’s Yvette Cooper, has opted not to table an amendment seeking to force the government to extend article 50, believing Conservative backbenchers are willing to give the prime minister another fortnight to continue negotiations in Brussels.

Instead they published a revised bill, backed by senior Conservatives Caroline Spelman and Oliver Letwin, aimed at preventing no deal – and promised to table an amendment on 27 February, forcing the government to make time to pass it.

“This bill creates a parliamentary safeguard to prevent us drifting into no deal by accident, and to prevent those crucial decisions being left until the final fortnight. The risks to jobs, the NHS and security from no deal are too great for us to stand back and let the government drift,” Cooper said.

The new amendment is likely to be the vehicle for Conservative MPs keen to prevent the prime minister from running down the clock and increasing the risk of an “accidental” no-deal Brexit.

Labour has tabled its own amendment to Thursday’s vote, putting in black and white her pledge to hold another amendable vote by 27 February, if she has not secured support for her deal by then.