With Theresa May donning her walking boots and heading for Switzerland, we have reached the breathing space that British politics has craved ever since the EU referendum. But we should enjoy it while we can, because it will be short. As soon as May returns from the Alps, speculation about an early general election, already widespread, will accelerate.

This chatter will be irrepressible. But in my opinion it will all be wasted energy. It is absolutely not May’s style to be looking for an early general election so soon after taking office. Her instincts, on this as on other matters of governance, are impeccably traditional. She believes the Conservative party won a mandate in May 2015, which she has inherited from David Cameron. She is personally untroubled by tabloid talk of needing to win her own mandate. Purists will say she is absolutely right about that.

What’s more, May is on the record as having said there would be no snap election under her leadership anyway. She said it on 30 June at the Royal United Service Institute in the speech that launched her bid to succeed Cameron. It’s there in black and white. She said it because she meant it, and in part because the markets needed to hear her say it so soon after the Brexit vote. Anyone who thinks that May is the kind of politician who says something so important without meaning it underestimates her, as many do.

Nevertheless, May cannot wholly ignore the political and journalistic culture that she currently commands. Already, in the early weeks, there has been plenty of speculation about an early election, including yesterday in the Times by the no longer quite as influential as he was Tim Montgomerie. Labour’s leadership contest has partly been triggered by the fear of just such a snap poll.

Facebook Twitter Pinterest Harold Wilson in 1970, the year he called an early general election – and lost. Photograph: PA

That talk is going to grow louder this autumn. Unless May utterly quashes the speculation, it will be the rumbling descant to the Tory conference in Birmingham in October.

True, that speculation will mainly come from the press, many of whom still don’t get it about May. The idea that a prime minister who takes over in mid-term is somehow illegitimate without a fresh mandate is a recent media conceit. It exemplifies a culture in which the media force politicians to jump through hoops. May, who is attractively disdainful about the media, will not be too troubled by that.

Her backbenchers are another matter. Politicians rarely go for long without thinking about re-election. And a lot of Tory backbenchers are excited by the prospect of increasing the majority. The idea of hitting Labour while they are down, of seeing off Ukip before they can regroup, and of giving themselves more Brexit breathing space before having to go back to the voters is inevitably attractive.

If the Tory opinion poll lead over Labour holds up at its recent double-digit level into the autumn – and this week’s polls offer conflicting evidence on that – election fever will increase. Pollsters will start asking about an early poll, Tory politicians will start being quizzed about one, and despairing Labour MPs may even start pleading for one, in the hope that Jeremy Corbyn would finally have to quit in the aftermath.

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There are, though, three immensely powerful reasons, in addition to May’s own instincts, for caution. The first is that an early election is unnecessary. Prime ministers call elections either because they lack a majority, or because they have used up their legislative energy, or because they face a defining crisis. None of these conditions applies today; May has a majority of 17, there are more than three full parliamentary sessions still to run, and the Tories could not currently face less of a challenge than they do from Labour.

The second is that the public dislike early elections. Voters take their responsibility seriously. They also seem to have a collective inner sense of whether an election is appropriate or not. Harold Wilson in 1970 and Ted Heath in 1974 both fell foul of that instinct, defeated in part because voters thought they were being called to the ballot boxes prematurely and for opportunistic reasons. Gordon Brown, if he had called an election in 2007, might well have discovered the same thing. An election this autumn or next spring would be even more premature and opportunistic.

Which leaves the final, and most insurmountable objection of all: that the law effectively prevents it. Under the Fixed-term Parliaments Act 2011, the prime minister no longer has the power to call a general election off his or her own bat. If May wanted to call an early election she would therefore face daunting parliamentary and political hurdles before she could do so.

Voters know when an election is appropriate. Harold Wilson and Ted Heath both fell foul of that instinct

To comply with the act, she would have to ensure that two-thirds of MPs, 433 of the current 650, supported her. Even supposing that all 330 Tories did so, she would still need Labour votes. Yet why should Labour MPs become willing martyrs in an election that by definition the Tories thought they would win handsomely?

The only alternative allowed by the act is for the government to contrive to lose a vote of confidence, confident in the knowledge that 330 Tories could then prevent another party forming an administration. That sort of Westminster game would be a hard sell to an electorate that already heartily disdains the political class.

That leaves two options: first, simply repealing the 2011 act, which some constitutional specialists think would not restore the power to call an election to the prime minister anyway; or, second, passing a bill specifying that the next election will take place on such-and-such a date, in spite of the provisions of the 2011 act. Ideally, the act should indeed be repealed. But May’s current honeymoon would struggle to survive the legislative shenanigans that such an effort would inevitably involve.

So it could hardly be plainer. There isn’t going to be an early election. Theresa May should say again, categorically, that there will not be. She would have been wise to say this before she headed for the hills. But she should say it as soon as she comes back to London at the end of the month.