A Football Association spokeswoman said England stood "shoulder to shoulder" with its European colleagues and "fully support the collective view".
She added: "We oppose Fifa's plans - the Fifa World Cup belongs to football and always will."
The Scottish FA added its support, saying its board "agrees unequivocally with the concerns raised by all members over the manner in which these proposals have been issued, and deadline set, without a full consultation process or consideration to good governance".
Scottish FA president Mike Mulraney is also the chair of Fifa's finance committee.
Culture Secretary Lisa Nandy said: "This is a principled decision that we strongly support. Football belongs to the fans, not billionaire investors. Enough is enough. It's time to take a stand to protect our game."
UK Prime Minister Andy Burnham criticised the plans on Tuesday, saying going ahead with the idea would mean Fifa had "sold out".
Concacaf said its members "expressed deep concerns about the lack of due process surrounding the proposal" and the "artificially short deadline imposed".
It also questioned the need for private investment after the most profitable World Cup in history, according to Fifa.
Concacaf added that it has tasked its Fifa council members with engaging the governing body on how to use existing reserves to fund development across the region and instruct Infantino to ensure proper governance processes are followed.
Ronan Evain - executive director of Football Supporters' Europe - told the BBC that Uefa's stance was "very impressive" and a "proper show of force".
He added: "It is the response that football needed - it is the response Gianni Infantino deserved."
The Asian Football Confederation said it was "disappointed" it had not been consulted before the plans entered the public domain.
The Confederation of African Football said its president Dr Patrice Motsepe would host a meeting of its executive committee next week to "assess and evaluate" the proposals.
The World Leagues Association (WLA) asked Fifa to withdraw its project and the Premier League, which is a WLA member, said it "wholeheartedly endorses" that view.
