FBI investigators have obtained a letter from João Havelange, who Mr Blatter succeeded as Fifa president in 1998, stating that the current head of football’s world governing body was aware of $100m (£66m) being paid to Fifa officials.

The alleged evidence, reported by the BBC’s Panorama, relates to vast sums paid by the Swiss sports marketing company ISL to top staff, including Mr Havelange and his son-in-law, the former Fifa executive Ricardo Teixeira. It is said that, in return, ISL was granted TV and marketing rights for most of the 1990s.

In the letter, Mr Havelange states: “During the period of time in which I was Fifa president, Mr Joseph Blatter was the secretary-general. I maintained commercial relationships with sports marketing companies which were under my economic control, and, as a result of these relationships, I received remuneration.”

He claimed the payments were made “in accordance with Fifa regulations” and added: “I emphasise that Mr Joseph Blatter had full knowledge of all activities described above and was always apprised to them.”

The letter from Mr Havelange emerged as a result of a request for information made by the FBI earlier this year to Swiss authorities, and is revealed in a Panorama documentary to be broadcast on Monday evening.

It is claimed that, despite his repeated denials, Mr Blatter knew about the payment of bribes. Two years ago, Mr Blatter told a Fifa ethics committee inquiry he was unaware of the bribery.

Mr Blatter is already under investigation in Switzerland over a £1.3m payment which the Uefa president Michel Platini received from Fifa in 2011, and over the sale of World Cup TV rights to the former Fifa vice-president Jack Warner.

The documentary also features Alexandra Wrage, a former member of Fifa’s reform committee, who says: “The structure allows you to make deals and take care of your cronies and trade in favours and it’s a really good gig.”

She adds: “Fifa absolutely can’t reform itself. It has failed utterly to reform itself.”

Meanwhile the Conservative MP Damian Collins, a member of the Culture, Media and Sport Select Committee, has said senior Fifa officials are “common criminals” who thought they were above the law. He likened the football body to a “corrupt Soviet republic” and added: “I think the Fifa republic is on the brink of collapse now.”

And the former England striker Gary Lineker said: “It makes me feel nauseous at the levels of corruption in a sport that has been a huge part of my life.”

The football body has faced demands to replace Russia and Qatar as hosts of the 2018 and 2022 World Cups, respectively, after The Sunday Times reported that 16 of the 24 committee members who had decided where the two tournaments should take place were currently under investigation or had been punished for misconduct.

A former director of public prosecutions, Lord Macdonald, said it was now “untenable” for the World Cup to be hosted by Russia and Qatar.

“The [US investigators’] ambition is to destroy Fifa as it currently exists and that’s because their view is Fifa is completely riddled with corruption,” he said. “They regard Fifa as an organised crime operation.” Last week US prosecutors charged 16 Fifa officials with committing a $200m fraud.

Asked by Radio Times if the organisation was turning a corner, former England captain David Beckham said: “No – they are just hitting the bend. There’s a lot still to be done. It’s such a mess that it’s going to take a while to sort out.”

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