Did the Conservatives steal the election by failing to declare local campaign spending? The short answer is no, but the longer answer is still interesting.

The allegation arises from the brilliant investigative journalism of Michael Crick, one of my heroes of political journalism ever since his exposure of Militant’s infiltration of the Labour Party in 1984.

The Tory election expenses story started in January this year when Crick discovered that the bills for a hotel in South Thanet were declared as costs of the party nationally, rather than as those of the constituency campaign. Spending limits for local campaigns are restrictive – £15,000 for the five-week election period – so the incentive to allocate the hotel bills, adding up to £14,000, to national spending is obvious.

South Thanet was the seat where Nigel Farage stood, so it was one of the places where the Tories concentrated their efforts. In the end, the Ukip leader’s challenge was defeated by a clear 2,800 votes. But now that result has been questioned and on Wednesday a judge granted the Kent police more time to investigate claims of illegal spending.

Meanwhile, Crick and his team at Channel 4 News have now found cases of possible undeclared spending by 29 Conservative MPs. Most of these involve hotel bills or the costs of battlebuses used to bring party volunteers into target seats.

The scale of the allegations has excited partisan Labour supporters. David Cameron has a working majority of only 16, so if eight Tory MPs could be disqualified, his Government would lose its ability to pass laws. Or, in the more extravagant vision, the result of last year’s general election would be reversed.

Liz Thomson, who was in the audience for Michael Gove’s grilling on Sky News on Friday, suggested to him that this would mean the EU referendum was “illegal”. This is the kind of thing that has been promoted on the internet by people demanding to know why the mainstream media, and in particular the BBC, has failed to cover the “Tory election fraud” story.

It has in fact been widely reported, Crick and Channel 4 News being part of the mainstream media. The reason it hasn’t been reported in the way that some people want is because nothing has been proved yet, and even if it were disqualifications and by-elections are unlikely. And even if the Conservatives were to lose enough seats to lose their majority – which is really unlikely – it would not have any retrospective effect on laws passed by the House of Commons, such as the one providing for the referendum.

Other things have also been reported, which are less useful for the “Tories stole the election” theory. There is evidence that MPs of other parties might have overspent on their election campaigns too. Cat Smith, the Labour MP for Lancaster, declared just one eighth of her election organiser’s salary in her constituency expenses, claiming he spent most of his time on national or council campaigns. A document apparently drawn up by Nick Clegg’s election agent, obtained by the Guido Fawkes website, seemed to suggest he had overspent in Sheffield Hallam. The Scottish National Party’s helicopter, which visited many constituencies during the campaign, was charged as a national expense.

Even if a breach of spending limits is proved in any of these cases, it would not necessarily mean a new election would have to be held. An election court could declare the election void, but if criminal charges were brought an MP would be disqualified only if he or she were sentenced to jail. In the only recent case, Fiona Jones, Labour MP for Newark, was found guilty of fraud in 1999 for failing to declare her full election costs, but her conviction was overturned on appeal.

If a court were to decide that hotel or battlebus costs should have been declared as constituency spending, what is most likely to happen, according to the legal blogger David Allen Green, is that national parties would have to pay large fines.

For the Conservatives, that would be humiliating for Andrew Feldman, the party chairman. Most people know him, if at all, as the subject of a video clip of Crick chasing him down Great George Street and Whitehall to ask him about election expenses after Crick’s camera operator said: “He’s legged it – he’s walked off the other way.”

It is in Lord Feldman’s embarrassment that the lasting significance of this story lies. The mood among Tory MPs is poisonous. One source tells me there is “huge resentment” towards the party chairman for his “complacency” in dealing with the allegations. It is not just the 29 Tory MPs affected by allegations of overspending, but the friends of the 29, among whom, I am told, many are “excoriating” about Feldman’s tenure at Tory HQ.

This is a problem for the Prime Minister, Feldman’s university friend, but also for George Osborne. When Tory MPs come to vote for the two-person shortlist for the next leader and therefore prime minister, it will be a problem for anyone associated with the Cameron-Osborne-Feldman regime.