One of Theresa May’s first acts as a Conservative leadership candidate was to rule out an early general election. After a tumultuous 2015 contest and the EU referendum, her view was that the country required a period of stability (a view shared by voters). Many newly-elected Tory MPs, fearful of a Brexit-inspired Ukip or Liberal Democrat surge, supported her on this condition.

After entering Downing Street, May reaffirmed her stance. “The Prime Minister could not have been clearer,” a senior source told me. “There won’t be an early election.” Maintaining this pledge is an important part of May’s straight-talking image.

But though No.10 has wisely avoided publicly contemplating an election (unlike Gordon Brown), the question refuses to die. The Conservatives have a majority of just 12 - the smallest of any single-party government since 1974 - and, as David Cameron found, legislative defeats almost inevitably follow. May’s vow to lift the ban on new grammar schools looks to many like an unachievable task. Former education secretary Nicky Morgan and former business minister Anna Soubry are among the Tories leading the charge against the measure (which did not feature in the 2015 Conservative manifesto).

To this problem, an early election appears to be the solution. The Tories retain a substantial opinion poll lead over Labour, the most divided opposition in recent history. An election victory would give May the mandate for new policies that she presently lacks.

“I don’t believe Theresa May wishes to hold an early election which there is evidence that the country doesn’t want and which, given the current state of the Labour Party, might be seen as opportunistic,” Nigel Lawson told today’s Times. “If, however, the government were to find that it couldn’t get its legislation through the House of Commons, then a wholly new situation would arise.”

It is not only Conservatives who are keeping the possibility of an early election alive. Many Labour MPs are pleading for one in the belief that it would end Jeremy Corbyn’s leadership. An early contest would also pre-empt the boundary changes planned in 2018, which are forecast to cost the party 23 seats.

For Corbyn, the possibility of an election is a vital means of disciplining MPs. Allies also hope that the failed revolt against his leadership, which Labour members blame for the party’s unpopularity, would allow him to remain leader even if defeated.

Unlike her predecessors, May faces the obstacle of the Fixed-Term Parliaments Act (under which the next election will be on 7 May 2020). Yet it is not an insurmountable one. The legislation can be suspended with the backing of two-thirds of MPs, or through a vote of no confidence in the government. Alternatively, the act could simply be repealed or amended. Labour and the Liberal Democrats, who have demanded an early election, would struggle to resist May if she called their bluff.

To many, it simply looks like an offer too good to refuse. Which is why, however hard May swats this fly, it will keep coming back.