Theresa May has drawn up plans for a secret charm offensive aimed at persuading dozens of Labour MPs to back her Brexit deal even if it costs Jeremy Corbyn the chance to be prime minister, the Guardian has learned.

Senior Conservatives say they have already been in private contact with a number of Labour MPs over a period of several months, making the case that the national interest in avoiding a no-deal outcome is more important than forcing a general election by defeating the government on May’s Brexit deal.

Now, with talks in Brussels entering their frantic final phase, the prime minister and her party whips are stepping up efforts to win backing for a compromise deal that one minister described as a “British blancmange”.

They are convinced they will need Labour votes to win, after a fractious Tory conference in Birmingham, at which determined opponents of the prime minister’s approach, including Jacob Rees-Mogg, won plaudits for saying they would vote against it.

One Tory source compared the challenge of striking a deal with the EU27 that would satisfy both sides of his own party to “landing a jumbo jet on the penalty spot”.

Labour MPs will thus be the focus of intense lobbying, in the period between May returning from Brussels with a Brexit deal and the meaningful vote, which is expected to come about a fortnight later.

Facebook Twitter Pinterest Street art depicting Prime Minister Theresa May by street artist The Pink Bear Rebel in Glasgow. Photograph: Jane Barlow/PA

Conservative whips are rehearsing an argument, the outlines of which were clear in the prime minister’s conference speech, that the deal on offer is a pragmatic one.

One cabinet member identified a string of Labour MPs they thought would take a “reasoned approach”, such as Chris Bryant, Rachel Reeves and Lucy Powell, politicians who have been critical of Corbyn in the past.

Bryant, a remainer, said he had not had any discussions with the government and would only be able to vote for a deal if May shifted towards Labour’s position of backing a customs union. Reeves said she had no intention of backing the government.

Privately, some Labour MPs believe at least 15 of their colleagues could vote with the government, rather than appear to their constituents to be trying to “block Brexit”, with up to 30, including some frontbenchers, prepared to abstain, rather than go through the voting lobbies with hardliners such as Rees-Mogg.

James Cleverly, the Conservative deputy chairman, has been liaising with some in this group.

May appealed directly to Labour backbenchers in her conference speech when she spoke of the “heirs of Hugh Gaitskell and Barbara Castle, Denis Healey and John Smith”, saying they were on the backbenches, not in the shadow cabinet of what she called the “Jeremy Corbyn party”.

She also told the party faithful that her deal “keeps faith with the British people” and was in the national interest. And she pointed to Sajid Javid’s announcement of a tougher migration regime as evidence that her approach delivers on the referendum result by ending the free movement of people.

Meanwhile, the EU is preparing to help May build a majority by offering Downing Street a written commitment to think again on “frictionless trade” if the UK changes its red lines after it leaves the bloc.

Facebook Twitter Pinterest May appealed directly to Labour backbenchers in her conference speech in Birmingham. Photograph: Mark Thomas/REX/Shutterstock

EU leaders want to throw the prime minister a lifeline in the long-awaited political declaration on a future deal, a first draft of which is expected to emerge next week.

If she clinches a deal with her EU counterparts in the face of formidable odds, May’s team believe the national mood will shift in her favour.

And they hope a positive bounce from the financial markets will help to convince some Labour MPs to hold their noses and back a deal based on Chequers – though she did not use the word Chequers itself in her speech.

Senior Conservatives have also been stressing the aspects of May’s approach that Boris Johnson and other hard Brexiters object to – including signing up to EU regulations in key areas.

Tory whips are also working on persuading a separate group of MPs from leave-voting constituencies, such as Caroline Flint, from Don Valley, and Gareth Snell, from Stoke-on-Trent Central.

Labour’s official policy is to reject any final deal that does not meet six tests drawn up by Keir Starmer, the shadow Brexit secretary, one of which is that it must offer the “exact same benefits” as membership of the single market and customs union.

Corbyn said in his conference speech that if the prime minister shifted her position on a customs union, and promised to uphold environmental regulation and workers’ rights, Labour could swing behind her. But his party is keen to secure the opportunity of pushing for a general election by voting down the deal.

A Labour source said: “Labour has been clear from the outset that if Theresa May’s Brexit deal does not meet our six tests then we will vote against it in parliament.” He added: “The Tories are wrong to say it’s a choice between Theresa May’s deal or no deal. No deal is simply not a viable option. There is no majority in parliament to take the UK off a cliff in March 2019.”

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The tight parliamentary arithmetic and the likelihood of a rebellion by the Tory right means that Labour votes will be vital, at least as an insurance policy, while having the additional benefit of encouraging a split within Labour.

But Conservative estimates vary as to how many of their own MPs would rebel in such a high-stakes vote. Losing it could unleash a constitutional crisis.

Steve Baker, the former Brexit minister, has suggested as many as 80 Tory rebels could vote against the prime minister, but Tory whips hope to “burn off” the majority, reducing them to around 10 diehards.

The government is also expected to argue that, while it will be possible to amend the final motion put before parliament, there is not enough time to delay article 50 and hold a referendum before the Brexit date of 29 March, because both would require primary legislation.

However, that has been disputed by second referendum campaigners who say the EU’s 27 member states would be willing to extend article 50 to give time for the UK to legislate for and hold a referendum if it were called for by parliament in the autumn.