The relationship between Uefa and Fifa has been tense during the World Cup, with the governing bodies clashing over the Folarin Balogun incident and other issues.
Uefa, Europe’s football governing body, said the decision not to uphold Balogun’s ban had “crossed a red line”, branding it “unprecedented, incomprehensible and unjustifiable”.
Fifa has faced criticism for the high cost of tickets to watch World Cup matches under its dynamic pricing system, and its response to Somali referee Omar Artan being denied entry to the US to officiate at the tournament.
The Liberal Democrats said these examples showed Fifa was “too far gone”.
Infantino defended ticket costs, arguing they were in line with other US sporting events.
There are 211 national football associations that are full members of Fifa, which organises the World Cup.
The English FA is a member of Fifa and if it withdrew from the governing body, 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”.
The “only route forward is for the FA, along with other European governing bodies, to lead a co-ordinated exit from Fifa”, he added.
Infantino has “crossed red line after red line”, Sir Ed says, accusing him of “allowing corporate greed to exploit fans at will, destroying the integrity of the beautiful game”.
“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.”
Football Action Network, a campaign group for football organisations, said there does need to be a debate about Fifa’s future.
“Nothing should be off the table if the game’s global governing body refuses to reform,” said Niall Couper, chair of the Football Action Network
Infantino’s presidency of Fifa has been controversial since he was elected to lead the governing body in 2016.
Supporters argue he has expanded the game and increased funding for member associations.
Critics say he has centralised power, prioritised commercial growth at the expense of fan experience, and weakened governance standards.
He is widely expected to have enough support from football associations to secure a fourth term as president, extending his tenure until 2031.
Anna Sabine MP, Liberal Democrat Spokesperson for Culture, Media and Sport said Fifa behaves “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,” Sabine added.