League Two side Tranmere said it “showed a total lack of respect”, while Peterborough chairman Darragh MacAnthony warned it could lead to a “fallout within English football”.

Greater Manchester Mayor Andy Burnham and Niall Couper, the chief executive of Fair Game, have sent a joint letter to Culture Secretary Lucy Frazer, and her shadow Thangam Debbonaire, which reads: “We know that many clubs in the lower leagues are battling to survive and these changes, if they were to proceed, would make that struggle even harder.

“Events of this season have led to rising concern among supporters at all levels that the football authorities are running the game in the interests of the few and not the many.

“Similar to the implementation of Profit and Sustainability Rules in the Premier League, these changes raise concerns about a lack of transparency, consistency and fairness on the part of the football authorities.

“If the new regulator is to be effective, it must be given powers to act to secure the health of the whole football pyramid.”

The Football Association insisted “all parties accepted” the change. However, the EFL urged the FA to “re-evaluate their approach”, stating there was “no agreement” prior to the deal being announced and no “formal consultation”.

Couper added that the move was “short-sighted and misguided” and that “elite clubs protecting their own narrow self-interest”.

He added: “The move is yet another example why football needs a strong and independent regulator that can ensure the financial future of our game.”

Fair Game’s amendment would cover other competitions – and if the changes were to change revenue distribution, then it would require approval by the independent regulator.

The Football Governance Bill, which would introduce such a regulator, is having its second reading on Tuesday and will go through a parliamentary process before it is made law.