Boris Johnson’s time as prime minister could, in theory, have lasted only a matter of hours.

Labour had been expected to table a vote of no confidence in the new prime minister yesterday, his first full day in No 10. If that had been successful, he would have been forced from office almost before he had even got his feet under his Downing Street desk.

In the end, the opposition decided not to table a confidence motion, threatening instead to do so when parliament returns in the autumn. Jeremy Corbyn said Labour would trigger a vote “at a time of our choosing” and “when appropriate to do so”.

The main reason for Labour’s decision to wait was that there was little prospect of the no-confidence motion being passed. While Johnson inherited a Commons majority of just two, it was unlikely that any Conservative MP would be willing to vote immediately to topple the leader that their party members had just elected.

Johnson also still has the support of the DUP. The Northern Irish party is continuing to prop up the Conservatives, although it has said that the “confidence and supply” arrangement it negotiated with Theresa May will be placed under “review” in the coming weeks. This is likely to be an attempt to secure new giveaways from the government for Northern Ireland, and it would be a major surprise, with potentially huge ramifications, if the party pulled its support for the Tories.

Might a no-confidence vote have a better chance of succeeding at a future date? The answer is a resounding yes. If Johnson pushes ahead with his threat to take Britain out of the EU without a deal, some pro-EU Tories who are currently biding their time would be much more likely to vote against the government in a no-confidence vote. That is their nuclear option for stopping a no-deal outcome, but some have already suggested that they would be willing to take it.

The realities of Brexit mean that Johnson’s honeymoon period as prime minister is likely to be short. While his critics on the Conservative back benches will give him the summer to prove himself, the Brexit deadline of 31 October means he will not be afforded long at all.

Whatever path he chooses on Brexit, he will anger some Tory MPs and opposition to his premiership will mount. That is when Labour is most likely to act.

Still, Corbyn’s refusal to try to topple Johnson’s government straight away has not been popular with some.

Jo Swinson, the new Liberal Democrat leader, called on her Labour counterpart to trigger an immediate no-confidence vote. When he declined to do so, she tabled an early day motion, the parliamentary equivalent of a petition, saying the Commons had no support in Johnson’s leadership.

This, however, is no substitute for a formal motion of no confidence in the government, and there is no sign that Labour is yet willing to try to force such a vote. The party dismissed the Lib Dems’ demand as a “childish and irresponsible game” and said that calling a no-confidence vote now would “only strengthen Boris Johnson’s hand and further his march towards no deal”.

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In theory, other opposition parties could try to force a vote but, under parliamentary convention, the government only has to allow time in the Commons for a confidence motion tabled by the official opposition party – currently Labour – meaning any motion put forward by the Liberal Democrats and/or other minor parties would almost certainly be ignored.

If a no-confidence motion was passed, a general election would be triggered after 14 days unless the Commons voted to say it had confidence in a new leader. This could be another Conservative who could unite the warring wings of the party, or it could be Corbyn. It could, in theory, be the same prime minister who had been toppled days earlier.

According to the House of Commons library, a no-confidence motion would have to be passed in the first week of September – the first week back after parliament’s summer break – if there is to be a general election before the 31 October Brexit deadline.

Many people in Westminster think that a general election in the coming months is increasingly likely. What remains unclear is the circumstances that will lead to it. Will MPs topple Johnson as he tries to force through a no-deal Brexit? Will the new prime minister call an election in an attempt to overcome parliamentary opposition to his Brexit plan? Or will he take the UK out of the EU on time and go to the polls on the back of a wave of goodwill for doing so?