Theresa May will go to Brussels this weekend in the sure knowledge that by far the biggest battle she faces is with her own MPs in a little over a fortnight’s time when the deal is put to parliament for approval.

Any basic reading shows that the arithmetic against her is formidable: 85 Conservative MPs have declared they cannot support the Brexit agreement as it stands, amounting to roughly one in four of her party at Westminster.

Strip out the government ministers – the so-called payroll vote of 100 who the prime minister can bank on – and the proportion of hostile MPs rises to something closer to 40%. The party’s chief whip, Julian Smith, has an extraordinary task on his hands.

Not all those coming out against are dyed-in-the-wool Eurosceptics. Robert Halfon, an influential backbencher close to the home secretary, Sajid Javid, supported remain in 2016, but on Friday he declared on Facebook that he would be voting against May’s deal.

The MP for Harlow complained that May’s deal could leave the UK locked “in an open-ended customs arrangement”, and that he was unhappy about “the different arrangements for Northern Ireland” but above all because “I don’t believe we are getting value for money out of the £39bn divorce bill of taxpayers’ money”.

Damian Collins, who chairs the Commons culture select committee, is another MP who had not been expected to pose a problem for May. “There is the opportunity for discussion and amendment right up until the final moment before the deal must be done,” he said this week. “Given we are not due to leave for another four months, I believe that there is still time to get this right.”

The Tory MPs who make up the 85 are those who have explicitly stated they will vote against the deal, or raised a string of objections. Others, who have not been counted in the Guardian’s analysis, have issued warnings that they are considering voting against without further reassurance, such as Grant Shapps and John Lamont.

Hardened sceptics include Iain Duncan Smith, Owen Paterson and Bernard Jenkin, whom the prime minister had hoped to coax over to her side by promising to pursue technological solutions to the Irish border. Duncan Smith and Paterson were name-checked in the Commons by May on Thursday but said minutes later any deal that includes the backstop would be opposed.

Richard Drax said he was losing faith in May. “Many of us feel we have been pushed to the limit of our patience, with a PM that simply does not listen,” he said in a blogpost. “There comes a time when, if someone simply does not listen and respond to the many, many warnings of a disaster, you begin to question your natural loyalty.”

Not all of the criticism has come from Tory Brexiters. The former ministers Justine Greening and Jo Johnson are among the Tories who have backed a second referendum, and say they cannot support May’s deal as a result. No wonder, in the words of one former cabinet minister, it feels like the prime minister is “heading towards a brick wall at 100 miles an hour”.