There are few sentences better able to lift the global mood than this one: "In four days' time, the World Cup begins in Brazil." The great festival of the beautiful game is a uniquely unifying force. Half of the world's population will watch some of the tournament, enthralled not just by parochial hopes of victory – England, obviously, once again, despite everything, just a little bit, expects – but by the special romance of a tournament in the nation that has become synonymous with its most sublime moments. As even the most Ukip of our face-painted travelling army of fans would have to concede, this time football really is coming home.

Brazil's World Cup will no doubt prove a joyous collective distraction from harsher realities. One man who has been counting on that fact more than most is Joseph "Sepp" Blatter, the 78-year-old president of Fifa, the game's global bureaucracy. The former PR man for a Swiss watchmaker, Blatter knows a good deal about precision timing. It is no coincidence that in this most feelgood of footballing weeks he will, against previous statements that he will step aside, put himself forward to the governing body for re-election for a further four years from 2015, probably unopposed. Neither does it appear without design that the one event that could have derailed that election process was also set to be announced while the footballing world was gathered round a TV, looking the other way.

Michael Garcia, who carries the oxymoronic title of Fifa's ethics investigator, has been looking for the past two years into allegations of corruption in the award of the 2018 and 2022 tournaments to Russia and Qatar respectively. His investigation was timetabled, happily, to be completed tomorrow. He is due to publish his report immediately after the final match in Rio. That report will not, he has suggested, incredibly, take any account of the millions of documents, revealed in the Sunday Times last weekend, which show compelling evidence that the award to Qatar in particular was tainted by the widespread financial bribery of Fifa delegates. The leaked cache of documents has, Garcia says, appeared too late for him to consider. They would ruin Fifa's schedule.

The way Blatter's organisation conducts the billion-dollar business of the global game has long looked like a scandal in waiting. Fifa's secret ballots and unaccountable, barely scrutinised machinations make it, at best, an out-of-touch anachronism in the modern commercial world. What other organisation, which purports to be a force of progress and inclusion, would countenance a president who suggests that the women's game would be improved by female players wearing "tighter shorts and low cut tops"? Or, when confronted by the fact of criminalised homosexuality in Qatar, would make a joke suggesting that visiting gay supporters "refrain from any sexual activity" for the duration of the tournament?

Football, as we know, has the power to break down barriers of all kinds, to become that fabled universal language. But for all Fifa's efforts to extend the reach of that language to the world's four corners, Blatter has presided over an era in which the vast riches at the elite level of the game threaten to become symbolic not of a shared sporting culture, but of an undemocratic and corrupting oligarchy.

When a significant proportion of the Brazilian population protests against a home World Cup and demands to know why the tournament has been funded by predominantly public – rather than private – money as promised, you can't help feeling Fifa has once again missed the easiest of open goals. Blatter has urged Brazilian protesters "not to use football to further their demands", as if, against all evidence to the contrary, the game – and the £4bn which the tournament will generate – suddenly existed in a world of its own.

Fifa has blundered through many crises before, relying on its peerless goodwill-generator to deflect criticism. Unless proper account is given to this latest series of corruption allegations, however, any credibility it still possesses will be gone. A rerun of the Qatar vote, plus the urgent reform of the organisation that produced it, including a change of leadership, is the least that football fans and national authorities should demand. Even a World Cup should not be allowed to get in the way of that.