David Davis has written to Conservative MPs warning that the party faces “dire” electoral consequences if Theresa May continues to pursue a Chequers-style deal with the EU27.

As talks in Brussels reach their final, frantic stage, the former Brexit secretary’s pointed letter, sent to all his parliamentary colleagues, was one of a series of interventions on Tuesday by critics of the prime minister’s approach.

“No 10’s stated position that there is only a binary choice between her Chequers plan and no deal is not correct. A third way does exist,” Davis said, urging Downing Street to switch to advocating the Canada-style trade deal he has long preferred.

May told her colleagues at last week’s party conference in Birmingham: “Those of us who do respect the result, whichever side of the question we stood on two years ago, need to come together now.

“If we don’t, if we all go off in different directions in pursuit of our own visions of the perfect Brexit, we risk ending up with no Brexit at all.”

But with intensive talks taking place in Brussels all week, backbench MPs critical of May’s approach are making their views known. Brexiters inside May’s cabinet, some of whom lean towards a Canada deal, are also watching developments closely.

Those calling on May to “chuck Chequers” are concerned that the “common rulebook” will mean too much alignment with EU rules, and frictionless trade for goods will restrict the UK’s ability to strike future trade deals.

Davis insisted Chequers would fail to meet the government’s commitments to “take back control of our laws, borders, money and trade” and that the EU would either reject it anyway or “take it as a basis for significant further concessions”.

As Conservative MPs mull over whether they will back May if she brings back a deal to parliament in the next few weeks, he claimed voters would punish the Tories if they implemented Chequers.

“If we stay on our current trajectory we will go into the next election with the government having delivered none of the benefits of Brexit, with the country reduced to being a rule-taker from Brussels, and having failed to deal with a number of promises in the manifesto and the Lancaster House speech,” he said.

“This will not be a technicality, it will be very obvious to the electorate”.

Earlier, Steve Baker, who worked alongside Davis in the Department for Exiting the EU, used a BBC interview to claim that the European Research Group, of which he is deputy chair, could count on 40 MPs voting against the deal.

Baker said his original estimate of 80 potential rebels was “an accurate number”, but conceded efforts by party whips would be likely to halve it.

Cabinet sources have previously told the Guardian they believe the more likely number to be between 10 and 20 rebels, which would still leave the government needing to rely on Labour votes.

Baker hammered home his message in five videos, published on Monday, warning: “The government’s Chequers plan does not deliver a meaningful Brexit and the EU says it doesn’t work.” Britain must pursue Brexit, he added, because “freedom is the fountainhead of prosperity, virtue and dignity”.

Separately, the former chief whip Mark Harper, who has broadly supported the prime minister in the past, used an article in the Telegraph to warn that Chequers would not pass the Commons.

Harper, a former immigration minister, said the issue of the Irish border could be dealt with through technology and by building on existing infrastructure.

He warned that the compromises involved in accepting Chequers, which prompted Davis, Baker and Boris Johnson to resign, would not be the last concessions exacted by the EU as it seeks to protect the integrity of the single market.

“I expect that the EU will demand compromises which are likely to be unacceptable to the prime minister, cabinet and Conservative party.

“Why do I say this? Because it is exactly how the EU behaved when David Cameron was negotiating his deal with them before the referendum, and which I witnessed first-hand as government chief whip.

“Therefore, in my judgment, the most likely way of achieving the good deal we all want to see with our European neighbours is a Canada-style FTA already offered to us by the EU as the basis of a deal,” he said.