One of the biggest and most frequently told lies in the Brexit debate is that there is no majority in parliament for a no-deal exit. It’s true to say that parliament has voted to deplore the idea of leaving the EU without a deal – but it has yet to vote for anything to put in its place. But by agreeing, as most MPs did, to trigger the Article 50 process on 29 March 2017 without first putting any limits or brakes on the government, they in effect voted for a no-deal Brexit, with no guarantee that they would be able to prevent it.

One of the ways that Boris Johnson convinced Conservative MPs who feared that his Brexit strategy would result in an election was by arguing that parliament, for all its opposition to a no-deal Brexit in theory, would quail from the necessary measures to prevent it. For what’s it’s worth, Johnson’s strategy consists of making a series of demands that cannot be achieved through a negotiated deal with the EU.

Is he right? That the main topic of conversation in and around Westminster this summer has been the creation of a so-called government of national unity to prevent a no-deal Brexit suggests he might well be. The plan, such as it is, is that the various opponents of no deal would come together to appoint a new interim prime minister. The new government would prevent no deal by seeking an extension to Article 50 and then resolve Brexit. The story is closer to science fiction than political journalism, but anything will do during the days of late August.

In truth, there are so many obstacles to the government of national unity proposal as to render the whole thing ridiculous. But the single biggest hurdle is that no alternative government can take office without the support of all 247 Labour MPs, and yet no government led by Jeremy Corbyn can command a majority in this parliament.

The 11 MPs elected under Labour colours who have since voluntarily left the party to sit as independents or to join other parties don’t have a great deal in common politically, but they share an antipathy to Corbyn on foreign policy and security issues. That feeling is shared by Conservative opponents of no deal. They haven’t forgotten that there was a terrorist attack during the 2017 general election campaign and fear the consequences of putting a Corbyn-led government in office.

As for the Liberal Democrats, whose 14 MPs would also be required to make Corbyn prime minister, they too will never vote for a Corbyn-led unity government – or, as their leader Jo Swinson prefers to call it, an “emergency” government – for both tactical and ideological reasons. Tactically, the overwhelming majority of Liberal Democrat target seats are Conservative-held, and the party’s strategists believe that to make Corbyn prime minister, however temporarily, would hole their electoral hopes below the waterline. They have made purposeful strides establishing themselves as the ideal home for voters who want to stop Brexit and have no desire to lend credibility to Labour on the issue. Ideologically, they want to stop Corbyn, because Swinson believes he is both a Brexiteer and a manifestation of the rising tide of populism she considers it her mission to defeat.

So a unity government led by Corbyn is a non-starter. And prospects for an alternative government under a different leader backed by Labour are little better. Labour’s small band of longtime Brexiteers are far from guaranteed to support a different interim Labour prime minister, such as Harriet Harman or Keir Starmer.

In any case, Corbyn has no intention of giving way to allow another figure to become prime minister. Why? Because if Labour fails to win a majority at the next election, Corbyn fears that having stepped aside to allow for the creation of a temporary Labour government this time would make it harder to resist calls to do the same again on a permanent basis.

So, I repeat, there is no prospect of a unity government – yet the row over who would lead it and what it would do rumbles on. Why? In part, it’s because the potential of a cross-party government allows the broadcasters to focus on personalities, which they find easier to do rather than report on the dull but important legislative work being done in the background to frustrate a no-deal Brexit.

But it also serves the interests of the political parties involved. For Corbyn, it is an opportunity to remind Labour voters that the last time some of them swapped a Labour vote for a Liberal one they ended up with a Conservative-led government – and one with Swinson in ministerial office to boot. Team Corbyn believe that their path to victory lies in re-running the 2017 campaign and that the more Corbyn is a lonely voice against the massed ranks of the establishment, the better placed they are to achieve that aim: at least, that’s the theory.

For Swinson, it serves as a way to underline her credentials as a Remainer and to reassure former Conservatives that she won’t be Corbyn’s back-door route to Downing Street. That’s not because the two parties are in cahoots – the reality is that formal relations between them have never been worse. Even at the height of the coalition, Ed Miliband’s and Nick Clegg’s offices retained a formal line of communication in order to plot against the Conservatives. There is no equivalent relationship between Swinson and Corbyn.

But the trouble for both is that while their bickering is good politics for them in respect of their electoral targets at the next election, neither is certain of achieving their aims in this parliament. Corbyn’s hopes of stopping a no-deal Brexit are slim, and Swinson’s hopes of stopping Brexit are slimmer still. For both of them, electoral success might prove to be a hollow consolation for political failure.