Why is world sport so corrupt? Olympics, football, cycling, even cricket have been enveloped in scandals of doping, match-fixing, transfer bungs and venue bribery. The Sunday Times' exposure of alleged corruption in Fifa's choice of countries to host the 2018 and 2022 World Cups is overwhelming. Yet Michael Garcia, the American lawyer appointed by Fifa to inquire into previous similar allegations, has said he will ignore it. His inquiry is rendered a farce.

The further any public activity drifts from accountability, the more it invites suspicion. When the activity is as popular and profitable as international sport, the scope for venality seems limitless. Distant oligarchies write their own constitutions and account only to equally introverted national associations. They seem immune to criticism or pressure to reform, many of them ensconced in Switzerland's haven for the secretive and the tax averse.

All that is new in the Sunday Times revelation is the weight of the evidence, seemingly millions of emails leaked by a whistleblower and strongly denied by Qatar. Fifa itself does little but organise World Cups, amassing a revenue reserve of $1.4bn in the process. Yet its history since 2006, when the maverick journalist Andrew Jennings began his inquiries, could be a script for The Godfather. Jennings's allegations, followed up by Panorama and the Sunday Times, are a catalogue of slush funds, kickbacks, bribes and favouritism. Commercial offshoots are said to be run by insiders and family members of the Fifa president, Sepp Blatter.

Fifa's claim is that host countries benefit from its blessings. The audit on South Africa's 2010 World Cup showed it cost the taxpayers £3bn for a return of £323m and an economic slump. This month's extravaganza in Brazil, which was pledged to cost the ill-resourced country nothing, has seen state spending on stadiums alone of £2bn, with another £9bn on infrastructure. Qatar is reputed to be spending a staggering £120bn. These sums for a brief sporting festival are obscene, whoever is paying.

To each and every accusation of corruption, Fifa gives a flat denial or a "not proven". Blatter casts aside rivals, critics and gross offenders, such as the Caribbean's Jack Warner, if they blatantly tarnish the image of his "family within". Bigwigs such as Henry Kissinger, Johan Cruyff and Lords Coe and Goldsmith are occasionally invited to dust Fifa with an aura of ethical sanctity. But when stories emerge of $40,000 in hundred-dollar bills laid out for Fifa's Caribbean supporters, Fifa blithely explains them as "intended for distribution to the poor".

The chickens of Britain's humiliating bid to "win" the 2018 World Cup are coming home to roost. The bid meant cringing subservience to the villain of the piece, Qatar's Mohammed bin Hammam, inviting him to Downing Street and Windsor Castle to meet the Queen, which he snubbed. It meant forcing the FA chairman, David Triesman, to resign for "inadvertently" hinting at Fifa corruption. It meant trying to censor the BBC for broadcasting similar "unhelpful" revelations on the eve of the 2010 vote.

David Cameron, the Duke of Cambridge and David Beckham, proclaimed as the "three lions", went in person to lobby Fifa board members before the vote in Zurich, despite newspaper warnings that it had been fixed. Vladimir Putin, who clearly knew he had already won, did not bother turning up. Cameron and Co were left looking like small-time bootleggers who had tried to outsmart Al Capone and were lucky to have escaped in the gutter with just a few broken limbs.

Successive evidence from Fifa whistleblowers over the past eight years has been damning. Yet until Britain was worsted in 2010, it parroted Blatter's defence of "not proven", fearing to lose any favours in its race for glory. The FA chairman Greg Dyke, 2018 bid executive Andy Anson and Commons sports committee chairman, John Whittingdale, now profess their shock at the allegations in the Sunday Times. But such allegations have been in the air for years. Why no shock from 2006 to 2010?

The one sanction against an international body is for its members to boycott it. The American soccer authorities, to their credit, have said they will not bid for any tournaments until Fifa is reformed. Yet Britain apparently wants to return to the same snake pit. With the decisions on 2018 and 2022 possibly now in abeyance, they are drooling at the prospect of becoming the venue by default.

"Winning" a World Cup used to be about a game of football. Now, as George Orwell said, it is war without the shooting, "bound up with hatred, jealousy, boastfulness and disregard of all rules". When winning is no longer a matter of sport but of national pride, it comes to seem a grinding national necessity. When glory is at stake, expense is no object and government goes mad. The heads of the IOC and Fifa are greeted like heads of state. Firms that make millions from these mega-events have ministers dance attendance on them. It is small wonder that priorities are so distorted as to ludicrously "award" a football tournament to Qatar in high summer. Even Blatter now calls that "a mistake".

Unreasoning government is always dangerous. When unreason is fed by corruption, and corruption goes unpunished, the only sensible response is to give it a wide berth. Britain should have nothing to do with Fifa and Blatter's "inner family". It should refuse to participate in venue bidding and withdraw from Fifa unless Blatter goes and his organisation is reconstructed. That should be obvious.

Yet this is unlikely to happen unless a critical mass of nations is prepared to form a rival world body. Britain, the birthplace of football, should be the initiator. At present neither its football authorities nor its craven government has shown the guts. Blatter knows it, and will rely on Britain to continue appeasing his benighted organisation. The only hope is that the World Cup's current extortion of billions of dollars from poor Brazil will bring other members to their senses.

Meanwhile, we might hear it for the one institution that has had the professional courage to call these monsters to account. That is not governments or regulators or lawyers or sportsmen. It is the old-fashioned British press. It is one World Cup I am proud for Britain to win.