Key pro-Brexit Tory MPs suggested on Saturday night they would be prepared to back Rishi Sunak over any “sensible” deal on the Northern Ireland protocol as the prime minister battled to limit any rebellion by Conservative backbenchers. Several leading Conservatives, who were prominent in the 2016 leave campaign and who had strongly opposed Theresa May’s attempts to broker a solution, said what Sunak was prepared to put to parliament seemed to represent clear progress. They said the number of Tories who might vote against the deal, which could be announced to parliament as early as Monday, was likely to be limited to between 20 and 40 hardcore anti-EU MPs. Hardline Brexiters reject this, saying that when colleagues see the extent to which EU law will still apply in Northern Ireland, particularly to businesses sending goods to other parts of the UK, many more will oppose it. Former Brexit secretary David Davis, who resigned from the cabinet over May’s Brexit deal, told the Observer that he had not seen details of Sunak’s agreement yet but made clear he did not expect to oppose it: “My instinct is not to vote against it if it looks anything like reasonable.” Davis said Sunak was attempting to undo the damage that, in his view, was done by Theresa May when she “conceded full alignment of north and south (of Ireland)”. He added: “What he [Sunak] is doing is not a complete reversal of the damage done but it is a significant reversal.” Another senior Tory backbencher and committed Brexiter, who is aware of opinion on the backbenches, said he thought most MPs accepted that the deal might not be perfect, but still represented progress. “If people were prepared to accept the protocol in the first place, they should be able to accept something that is an improvement on it,” he said. “Most people do not think this is the time to be causing political problems for the PM.” Martin Vickers, a member of the 1922 executive and longstanding Eurosceptic, said it was time to “move on” and address issues the electorate cared about. Tory MPs have been on a three-line whip for Monday, raising expectations that Sunak will present his deal to the Commons then. Under the changes to the post-Brexit rules for Northern Ireland agreed between London and Brussels, most checks and paperwork on goods crossing the Irish Sea would be scrapped. But EU law would still apply in many respects as Brussels insists it must to protect the single market. Despite signs that some Eurosceptics are coming round to the deal, there is still nervousness at No 10 about the role of Boris Johnson in stirring up dissent. One Tory MP, who is undecided on how to vote, said the size of any rebellion could be doubled should Johnson oppose it. The former prime minister has spent the past fortnight talking to supporters, the DUP and the Eurosceptic European Research Group over the government’s plans, as well as his protocol bill that will be abandoned should Sunak press ahead with his deal. Figures close to Johnson are keen to play up possible rebellions, saying that his involvement could well mean the government would need to rely on Labour support to win any vote on the new deal, a development some have described as “political suicide”. There are also warnings of government resignations. “I’ve spoken to someone who is clear that if the European Court of Justice is still involved, they will quit,” said one wavering MP. It is thought that Sunak has secured an agreement that allows the UK government to set VAT rates and state aid policy for Northern Ireland, rather than this being a matter for the EU. Downing Street was refusing to say on Saturday night whether a deal would be put to parliament this week, and when there might be a Commons vote. Figures in the ERG have been frustrated by the secrecy. “We can’t agree on anything without seeing the text – nobody could be expected to,” said one. “Obviously we’d love to support it. But it would be a huge shame if it didn’t result in the restoration of the institutions in Northern Ireland, or if we find ourselves in the same position in two years.” Another Tory MP, who is undecided on the issue, said No 10’s secrecy was causing distrust within the party. “It makes me wary,” they said. “Is there something that they don’t want me to see, that’s going to be thrusted upon us and we’re expected to vote on within 24 hours? “They’re hoping that it will just be the diehard Brexiters, who they can label as the Looney Tunes squad, that will rebel. But if you get 35 to 40 people, that’s a problem. If Boris rebels, it could reach that number.”