Relations between UEFA and FIFA were tense during the World Cup as differences arose between the governing bodies over the Folarin Balogun incident and other issues.
UEFA, European football’s governing body, said the decision not to support Balogun’s ban had “crossed a red line”, calling it “unprecedented, incomprehensible and unjustified”.
FIFA has been criticized for the high cost of tickets to watch World Cup matches under its dynamic pricing system, as well as its response to Somali referee Omar Artan being denied entry into the US to officiate at the tournament.
The Liberal Democrats said the examples showed FIFA had “gone too far”.
Infantino defended ticket prices, saying they were in line with other U.S. sporting events.
211 national football associations are full members of FIFA, which organizes the World Cup.
The English FA is a member of FIFA and if it leaves the governing body, England will not be able to participate in the World Cup.
Sir Ed said football associations must work together “to create a clean and transparent governing body that puts fans first”.
“The only way forward is for the FA, together with other European governing bodies, to lead a coordinated exit from FIFA,” he added.
Infantino has “crossed red line after red line”, says Sir Ed, accusing him of “allowing corporate greed to exploit fans at will, destroying the integrity of the beautiful game”.
“It is time for UEFA to leave FIFA and start working with other confederations to create a clean and transparent governing body that puts fans first.”
The Football Action Network, a group that campaigns for football bodies, said a debate about the future of FIFA was really needed.
“Nothing should be ruled out if the game’s global governing body refuses reform,” said Niall Cooper, chairman of the Football Action Network.
Infantino’s FIFA presidency has been controversial since he was elected to lead the governing body in 2016.
Supporters say he expanded the game and increased funding for member associations.
Critics say he has centralized power, prioritized commercial growth over the fan experience and weakened governance standards.
He is expected to receive enough support from football associations to secure a fourth term as president, extending his term until 2031.
MP Anna Sabina, the Liberal Democrats’ spokeswoman for culture, media and sport, said FIFA was behaving “more like a closed cartel than a neutral global sporting body”.
She said: “By claiming 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 honesty, not four more years of unchecked cronyism,” Sabina added.