Nine years ago this month, Scotland Yard launched an investigation into the alleged sale of honours by the Labour party.

Angus MacNeil, an SNP MP, claimed that Tony Blair’s party was giving peerages in return for donations and often undeclared loans. Over a 16-month investigation, a sitting prime minister was formally interviewed by the police for the first time, while a series of political aides and donors was arrested; accusations and counterclaims were made through the media. Then nothing.

The Crown Prosecution Service announced in July 2007 that there was insufficient evidence for a prosecution. Crucial evidence of any actual agreement struck between party official or politician and a donor leading to a gong had not been found.

This weekend in a groundbreaking study with profound implications for the country’s democracy, Oxford University’s website is hosting a working paper containing meticulously compiled statistical ammunition for those who believe that the issue should be revisited.

Conservative party donors made peers. The donation tallies for all the donors include sums given by them, their families, unions or companies.

The research, entitled Is There a Market for Peerages? Can Donations Buy You a British Peerage? A Study in the Link Between Party Political Funding and Peerage Nominations, 2005-14, is the most exhaustive cross-party examination of the correlation between donations and peerages ever undertaken.

It offers no “cast-iron proof that any peerages have been sold”; all the major donors to the parties who have subsequently received a nomination for a peerage have impressive credentials that cannot be ignored; in terms of donations and honours, correlation is not the same as causation. And even if it is proved that a peerage came as a reward for a donation, there is nothing necessarily criminal in that.

But, for the first time, the academics say that statistically it can be said that the “relationship between donations and nominations [for peerages] has been found to be significant”. A debate, they say, about whether we are comfortable with that needs to be had.

The academics examined the 303 Lords nominations between 2005 and the third quarter of 2014 and all donations since 2001. They isolated what they term the “usual suspects”: prominent people who would be expected to be in line for an honour, such as former parliamentarians, senior party staff, ex-council leaders, reserved public sector posts, “people’s peers” nominated by the House of Lords Appointments Commission, and those selected as part of Gordon Brown’s “government of all talents” agenda.

That left 92 “others”, who donated between them 97.9% (£33.83m) of all the donations coming from nominees to the Lords. Donations from the individuals’ companies, spouses or children were included. In the case of union leaders, the donations were generally from their unions rather than themselves.

Lib Dem donors made peers or nominated for peerages. Parminter donated £5,400 under her own name, while her husband donated £122,672.27 and the remaining amount was donated by KPMG when her husband was a partner. Choudhrie’s planned nomination for a peerage was withdrawn. The donation tallies for all the donors include sums given by them, their families, unions or companies.

Among those, 27 donated 95% of the £33.83m. The academics write: “Clearly, those peers nominated outside the ‘usual suspects’ are far more likely to be big donors.” The 27 came from a larger pool of 779 big donors who stood out on electoral commission records.

The academics ran the calculation of how probable it would be that from a random sample of 779 people from a pool of available nominees – defined as the 383,000-strong reported membership of the three main political parties – 27 or more would be nominated to the Lords between 2005 and 14.

In what they hope will be the opening shot in a debate about the state of British democracy, the academics – Dr Andrew Mell of Corpus Christi College, Oxford; Simon Radford, of the University of Southern California; and historian Dr Seth Alexander Thévoz – conclude the probability of such an outcome is “approximately equivalent to entering the National Lottery and winning the jackpot five times in a row”. They say that this is wholly in keeping with the argument that lifetime appointments to Britain’s upper house are in effect being sold.

They also found that individuals drawn from the “others” donated an average of a further £220,000 among Conservatives, £333,000 among Liberal Democrats and £464,000 among Labour nominees. If peerages are in effect being sold, the academics argue, “these could be thought of as the ‘average price’ per party.”

Former Liberal Democrat peer, Matthew Oakeshott, who on leaving the Lords in May last year lamented that his efforts to uncover cash-for-honours deals across the parties had failed, told the Observer that the case against the system, and the parties, was now compelling. Yet, in reality, constitutional reform is unlikely to be top of the agenda of any of the major political parties in the run-up to the general election. In the 2011 referendum on adopting a form of proportional representation, only two in five of the electorate bothered to vote. More than two-thirds of those (67.9%) voted for the status quo.

There have been a series of political scandals in recent months: the Channel 4 sting on Jack Straw MP and Sir Malcolm Rifkind MP, during which the former cabinet ministers allegedly offered their services to a fictitious Chinese company; claims of tax avoidance by Tory donors; suggestions that Labour wanted to keep secret the identity of a hedge fund backer secret; and the resignation of a Lib Dem peer on Friday over claims that donations were given for access to Nick Clegg. All serious issues. Yet they have hardly provoked any significant public clamour for reform.

It is, it would appear, within Westminster that the drive for reform must come – and those working there are well aware that something is seriously wrong.

Labour party donors made peers or nominated for peerages. Donations for Drake and Morris were made by their trades unions. A significant amount of Gerrard, Townsley and Patel’s donations were made as loans; and their peerages were blocked. The donation tallies for all the donors include sums given by them, their families, unions or companies.

Speaking to a packed Lords committee room 4a, in an upper corridor in the Palace of Westminster, Lord Cormack, who first stood as an MP in 1966, was a candidate to replace Betty Boothroyd as speaker of the Commons, and who was made a life peer in 2001, is said to have made a telling comment. “The biggest abuse is putting party donors into the House of Lords,” he said, according to one of the academics behind today’s research at the 2014 meeting. “This has happened from all three parties, even in the last five years.” Approached by this newspaper, Cormack declined to comment. He said he had been talking in a “private meeting”.

In a lecture a year earlier, David Steel, former leader of the Liberal party, went further in a condemnatory lecture on the decision to leave the power of patronage in the hands of the party leaders. “That means,” he said, “not surprisingly, each party leader finds that those doing nothing for the party except writing large cheques somehow manage to catch their eye.”

The spur for today’s research was an intriguing conversation some years ago between a life peer and one of the academics, Seth Thévoz. “I was working as a parliamentary researcher for a Lib Dem MP, and with the wages being pretty low I stuck an ad on a House of Commons notice board offering my services moonlighting as a speechwriter,” Thévoz told the Observer. “I received an answerphone message from the secretary of a peer in a different party.

“His secretary summoned me to meet him [the peer] at the Peers’ Entrance. He took me up to the Royal Gallery, adorned with tapestries, and we perched at a desk there – he explained he lacked an office at the time. He didn’t know me at all, and I was shocked by what he told me within three minutes of meeting me: ‘I only joined this party a couple of years ago, but look where I am today! I’ve put every penny I have into getting here [points to the ground], and look where it’s got me.’” When asked about the conversation, the peer told this newspaper: “He’s got it wrong, I didn’t say it.” Perhaps there is smoke in this case without fire. Statistically, however, we now know it is unlikely.

Nine years after the cash-for-honours investigation was launched, the SNP MP who sparked it all is reflective. “You would have to be a willing idiot not to see the correlation,” MacNeil said. “The police were left pretty down about it all last time. But if it isn’t criminal, it is wrong.”