Sir Ed Davey has called on the Football Association to withdraw from Fifa, accusing it of “destroying the integrity of the beautiful game”.
The Liberal Democrat leader said international football’s governing body no longer served the game or its supporters and should be dissolved.
He demanded that both the English FA and Uefa, the game’s European governing body, pull out of Fifa after it decided to overturn a match ban for an American player.
Earlier in July, Donald Trump personally contacted Gianni Infantino, the Fifa president, to request that Folarin Balogun be allowed to play in the US’s match against Belgium.
This year’s World Cup, which has been hosted by the US, Canada and Mexico, has also been dogged by complaints from fans over ticket prices – with prices for the final reaching $10,990 (£8,171) by April – and matches being interrupted by hydration breaks, which could generate up to $250m (£189m) in extra advertising revenue for Fifa.
Fifa also faced criticism after Mr Infantino refused to challenge the US’s decision to deny entry to Omar Artan, a Somali referee, to officiate at the tournament.
Uefa said the decision not to uphold Balogun’s ban had “crossed a red line”, calling it “unprecedented, incomprehensible and unjustifiable”.
The Liberal Democrats said these examples showed Fifa was “too far gone” for reform.
Mr Infantino has defended the tournament’s ticket prices, arguing that they are in line with other US sporting events.
In the unlikely event that the FA did withdraw from Fifa, England would not be able to compete in the World Cup.
Sir Ed said football associations should work together “to build a clean, transparent governing body that puts fans first”, adding that the “only route forward is for the FA, along with other European governing bodies, to lead a co-ordinated exit from Fifa”.
He said Mr Infantino had “crossed red line after red line” and “allowed the likes of Donald Trump to dictate on field decisions, whilst allowing corporate greed to exploit fans at will, destroying the integrity of the beautiful game”.
Sir Ed added: “It is time for Uefa to step up and walk away from Fifa, and start working with other confederations to build a clean, transparent governing body that puts fans first.”
The Lib Dems’ call also comes after the White House’s World Cup chief defended Argentine players who unfurled a banner claiming ownership of the Falkland Islands after their victory over England on Wednesday.
Fifa’s rules prohibit the display of political messages during the World Cup, and Downing Street has urged the governing body to investigate.
But Andrew Giuliani, the head of the White House’s Fifa taskforce, said on Friday that the US constitution’s free speech protections meant the Argentine team had a right to “make those statements”.
Earlier this month, The Telegraph revealed that the FA had decided to back Mr Infantino’s attempts to stay in power.
It is understood that Mr Infantino already has the formal endorsement of more than 200 Fifa members for a fourth term as president, extending his tenure until 2031.
A small number of European associations are understood to have yet to endorse him, including Germany.
Candidates must be put forward by Nov 18, before which time letters can also be withdrawn or transferred to a different contender.
Mr Infantino is the only candidate and football observers say it would take a political “earthquake” to unseat him.
Football Action Network, a campaign group for football organisations, said it was time for a serious debate over Fifa’s future.
Niall Couper, the group’s chairman, said: “Nothing should be off the table if the game’s global governing body refuses to reform.”
Mr Infantino’s presidency of Fifa has been controversial since he was elected in 2016. He has been accused of centralising power, prioritising commercial growth over the experience of fans and weakening standards of governance.
Anna Sabine MP, the Liberal Democrats’ spokesman for culture, media and sport, said Fifa behaved “more like a closed-shop cartel than a neutral global sporting body”.
She said: “By rubber-stamping a fourth term despite these toxic scandals, football’s governing bodies are showing they are content to sit in rotten squalor rather than strive for something better.
“Fans deserve transparency and integrity, not another four years of unchecked cronyism.”
Fifa, Uefa and the FA have been approached for comment.