Monday’s decision by Parliament to debate the funding of the Vote Leave campaign is likely to reignite a debate about Brexit. However, that debate is unlikely to amount to much.

The statement was driven by an interview broadcast on Channel 4 with former Vote Leave volunteer Shahmir Sanni. The former treasurer of BeLeave, another campaign organisation, Sanni claimed that Vote Leave sought to get around the spending limits imposed by the Electoral Commission’s rules in the EU referendum in 2016. They did this by donating £625,000 to BeLeave: this was not in of itself illegal, but the assertion that the groups coordinated their work made it so.

The logic of the non-coordination rule is simply that if all that limits a group’s spending is its nominal independence, then it offers no protection. Grassroots Out discovered this during the referendum itself, when opponents of Brexit argued that the multiple associated groups it established could not be counted as discrete units.

In the current case, Vote Leave and BeLeave shared offices, with the former also offering advice and assistance.

The former leader of Vote Leave, Dominic Cummings, wrote – with typical length – about the accusations, saying they were baseless, that the Electoral Commission had already investigated Vote Leave twice (without charge) and that this was just another case of sour grapes.

However, the announcement has gained some further momentum with the allegations that Theresa May’s political secretary Stephen Parkinson had outed Sanni as gay, as part of his (Parkinson’s) rebuttal of Sanni’s claims.

But the decision to allow a Parliamentary debate will give further opportunity for pushing this story and encouraging further action.

Clearly, any abuse of funding rules requires investigation, but the broader question that is raised is of whether the claim – if upheld – challenges the outcome of the referendum.

This breaks down into two basic elements.

The first is whether non-respect of the spending limits might materially affect the outcome. Even if the simultaneous debate about Cambridge Analytica produces more concrete evidence about the power of micro-targeting online campaigns, it is effectively impossible to prove that any given number of votes were mobilised or swayed because of that over-spent money.

Simply to pro-rata the Leave vote down by the percentage over-spend would be an indefensible position, given all the other campaign groups involved, not to mention the original grassroots activity that took place.

This means that the second element – the question of whether the referendum might be annulled and re-run – looks like a disproportionate response. Not only would it be seen as a highly political move by the Electoral Commission (who would have to make such a recommendation) and by the government (who would have to take it through Parliament).

Already, the referendum has been surrounded by questions on all sides. From the government sending out an official pamphlet advocating membership just before the start of the purdah period, to the endless arguments about the veracity of claims made by both official campaigns, there is already a high level of distrust. To then select one element as grounds for a re-run is thus politically dubious.

This all suggests that this is likely to end up as another instance of confirmation bias: supporters on both sides of the debate will feel that it reinforces their view of the world.

Hence, it will become another part of the narrative of pro-Remainers who feel that they were cheated by the referendum, with dirty tricks and sharp practice robbing them of a fair victory.

Likewise, for Brexiteers it will be a demonstration of Remainers’ inability to accept a democratic decision of the people.

Put differently, most people’s view of the referendum and its outcome is always pretty hard-baked. Even a more egregious overstepping of what is permitted will be unlikely to shift many attitudes.

This is not to say that this is not an important matter, but rather that the finances of a group in the EU referendum have to be set against the much bigger picture of how the UK is engaging with Brexit. And from that perspective, a wholesale review of our situation looks like a distinctly remote proposition.

Dr Simon Usherwood is the Deputy Director of The UK in a Changing Europe.