You cannot get rid of a Prime Minister just because she has a cough, but Theresa May’s unlucky speech yesterday did have the effect of focusing Conservative minds on the leadership question.

As Joe Watts reports today, there are Tory MPs who are trying to organise for a change at the top, and most of them would prefer Amber Rudd, the Home Secretary, to take over rather than Boris Johnson or David Davis. Rudd had a good conference, appearing to take control in the conference hall when May’s speech was disrupted by a joker.

But too few Tory MPs want an immediate change: there are maybe 30 to 35 of them, and it takes 48, or 15 per cent of the total, simply to trigger a vote of no confidence in the leader. That vote of Tory MPs is the only way to force a leadership contest if the leader doesn’t want to go, and even if there were 48 MPs who wanted May out, there are certainly not the 160 who would be needed to defeat her in that vote.

The scenario that worries many senior people in the party, on the other hand, is that May and her husband Philip decide that she has had enough. Gary Gibbon, the Channel 4 News political editor, reported yesterday that someone who “has worked with Theresa May for quite a long time” said: “She will turn round to the team and say, ‘It’s over.’ I’m sure she will.”

Whether or not that happens – and even if it does May could be talked out of it – there has been an urgency in the past few days in the planning for a sudden vacancy. Again, Rudd is interesting. Her decision to hire Lynton Crosby, the Australian consultant who won the 2015 election for David Cameron (and who helped to lose the 2017 election for May) was significant. She and Johnson spent time in hotel rooms during the conference meeting the donors who will make leadership campaigns possible – whenever they are needed. Many of the donors who supported Cameron are backing Rudd, I am told, certainly if there is a contest soon.

I suspect there will be a lot of pressure on May, if she is indeed having doubts, to stay on until Brexit happens in March 2019. The fundamentals of the Tory party have not changed just because one speech was a presentational disaster.

Theresa May's 'disastrous' conference speech – in pictures Show all 8 1 / 8 Theresa May's 'disastrous' conference speech – in pictures Theresa May's 'disastrous' conference speech – in pictures Prime Minister Theresa May arrives to deliver her keynote speech at the Conservative Party Conference in Manchester PA Theresa May's 'disastrous' conference speech – in pictures Comedian Simon Brodkin, dressed as a Tory party delegate, hands Theresa May a P45 during her speech PAUL ELLIS/AFP/Getty Images Theresa May's 'disastrous' conference speech – in pictures May suffering a coughing fit during her speech Reuters Theresa May's 'disastrous' conference speech – in pictures May wears a Frida Kahlo bracelet and holds a sweet passed to her by Chancellor Philip Hammond as she addresses the conference in Manchester Reuters Theresa May's 'disastrous' conference speech – in pictures May struggles with her water as coughing fits continued to interrupt her speech Reuters Theresa May's 'disastrous' conference speech – in pictures The wording on a slogan is changed after a letter falls away from the backdrop towards the end of the speech Reuters Theresa May's 'disastrous' conference speech – in pictures May is congratulated by her husband Philip, with the sign in the background missing a F and an E, after she delivered her keynote speech PA Theresa May's 'disastrous' conference speech – in pictures May is embraced by husband Philip after delivering her speech Getty

Most Tories do not want a leadership contest while the Brexit talks are going on. They feel they have already wasted a lot of time with a general election that went badly, and a leadership election would simply open up the divisions that are already uncomfortably wide.

And many MPs fear that a change of leader might mean another general election would become more likely. That is something they really do not want. Luckily for them, it is not going to happen. It is surprising how many parliamentarians do not understand the Fixed-term Parliaments Act. An early election can happen only if MPs vote for it, either by a two-thirds majority, as voted for the June election, or by a majority to repeal or amend the Act (or to express no confidence in the Government). Unlike in April, Tory MPs are not going to vote for an early election. Neither are DUP or SNP MPs. There is no majority for it, and not likely to be for some time, despite the eager hopes of some Labour supporters expecting “Corbyn by Christmas”.

It is dangerous, as Theresa May discovered during the election, to say, “Nothing has changed.” But one bad speech does not change the fundamental arithmetic of the Prime Minister’s position.

Letters fall off Tory slogan behind Theresa May during conference speech

Indeed, the presentational problems may have helped her, by distracting from the embarrassing thinness of the policy on housing. Subsidising the building of 5,000 social homes a year hardly lives up to her advance billing as a new Supermac – Harold Macmillan oversaw the building of 300,000 homes a year.