Tory MPs are preparing to challenge David Cameron’s leadership – even if they know they’ll fail

Maybe there are 50 Tory MPs who are headbangers, but are there 165? That is the number needed actually to dislodge the Prime Minister

It may be the torpor of a Bank Holiday weekend, but no normal person would have been distracted for more than a moment by the revelation that Nadine Dorries has a low opinion of the Prime Minister.

As long ago as 2012 she called David Cameron and George Osborne “two arrogant posh boys … who don't know what it’s like to go to the supermarket and have to put things back on the shelves because they can’t afford it for their children’s lunch boxes”.

It would have been more surprising if she had told Robert Peston yesterday that she hadn’t got round to writing to Graham Brady, the Chairman of the 1922 Committee of Conservative backbenchers, to ask for a vote of no confidence in the party leader.

But it is a Bank Holiday weekend, the to-and-fro on whether we send £350m a week to the EU or only half that has become tediously repetitive, and so a Tory leadership crisis is what we need for the front pages. Throw in some tasteless anonymous quotations and Andrew Bridgen, another Tory irreconcilable, and there is enough to fill a news vacuum.

Let us just remind ourselves of the rules, though. To mount a leadership challenge, 15 per cent of Tory MPs must ask the Chairman of the 1922, in writing, to hold a vote of no confidence. That is 50 MPs. So far we know of one, Ms Dorries.

There may be another 49 who dislike Cameron enough to write to Mr Brady. The letters are confidential – unless you go on TV and announce them – and Tory MPs trust Mr Brady to keep them so. Cameron is surprisingly unpopular for a leader who has delivered his party into government for at least 10 years. Nearly half of his parliamentary party want to leave the EU and will feel that Cameron has let the nation down by fixing it for Remain – that is, by running a ruthlessly effective campaign in what he sees as the national interest.

Then you get to the next stage, which is the vote of confidence itself. Maybe there are 50 Tory MPs who are headbangers, but are there 165? That would be the number required to produce a tie in the parliamentary party of 330. Formally, I assume a tie means that the status quo prevails, but in practice it would be the end of Cameron’s leadership.

But there are not anything like 165 Tory MPs who would bring down a leader who had just won a referendum and replace him with, in all likelihood, Boris Johnson, who had just lost it.

The upper bound for support for an early leadership change is 142. That is the number of Tory MPs who have publicly declared for Leave. (A majority, 172, have declared for Remain, and I suspect most of the 16 who have not declared are Remainers who don’t want to tell their local associations.)

That is why I am told the Prime Minister thinks that “there could be” a vote of confidence, but that “it wouldn’t be successful”. His message to the rebels is: “What’s the point? I’m going anyway.” But that is to assume that his critics would behave rationally.

The traditional constraint of an opposition party threatening their seats has been removed: they might just go for a pointless leadership challenge for the sake of it.