Such an arrangement is championed by leading Brexiteer Tories who say the Chequers blueprint, hammered out at the Prime Minister’s official country residence in July, will leave Britain a “vassal state” tied to Brussels rules.
Former Brexit secretary David Davis forecast last week that a similar number of up to 40 pro-Brexit Tory MPs would vote against Chequers which he resigned in protest at.
Yesterday some senior ministers were said to want Mrs May to consider a Canada-style deal if the EU continues to reject her plan for a common rulebook for goods and facilitated customs arrangements.
Sources said they feared her hardline stance against alternatives could force Britain into a no-deal Brexit “by accident”.
Mrs May has said that “no deal is better than a bad deal”.
This week she explicitly said that no deal would be better than the Canadian model, which she said would effectively break up the United Kingdom by keeping Northern Ireland in parts of the EU customs union and single market to avoid a hard border with Ireland.
The Prime Minister and her aides are clinging to the Chequers blueprint despite a humiliating rebuff by EU leaders at a summit in Austria last week.
Ms Rudd was asked on ITV’s Peston if she would support a “Canada-plus” deal on the lines backed by her party’s Brexiteer faction.
She said: “No. I have talked to a few colleagues and I reckon there are, conservatively, about 40 of us who would not support a Canada-type deal.
“There are so many reasons a Canada-type deal doesn’t work, starting with the Irish border, going on to manufacturing, that I think we can make those arguments. But that just reinforces the point that there is an impasse.
“The rebel group need to think again because I think we have only got one shot at a negotiated settlement.”
Ms Rudd said she did not expect Britain not to strike a deal with Brussels.
But if it could not, the country was in “completely uncharted territory”.
“One of the outcomes you might get is a Norway-style European Economic Area deal, and I know that various colleagues are looking at that.”
A second referendum, dubbed a “people’s vote”, would “absolutely” be better than a no-deal Brexit, said Ms Rudd.
In a warning to Brexiteer colleagues, the former home secretary added: “It would be ironic if we got a people’s vote because the more ‘Brexity’ people in my party were unable to support the Prime Minister in her negotiated settlement – and then they might not even get their Brexit.”