The EFL has said it is “eagerly” anticipating the introduction of an independent regulator for English football after it lamented the “repeated failure” of the Premier League to strike a deal on financial redistribution.

This week the Premier League was unable to carry its clubs to support a measure that proposed sharing more than £900m across the football pyramid. On Thursday the EFL board met to discuss its response, and concluded it was “more important than ever” that the proposed regulator had the power to force through a deal.

In a statement the EFL said it was “clearly disappointed at [Premier League clubs’] repeated failure to put forward any new funding offer for EFL clubs” and the lack of positive progress “once again demonstrates how difficult an issue this is for football to address, without independent input. The EFL has repeatedly said that financial redistribution coupled with enhanced cost controls are needed to help achieve its overriding objective of making EFL clubs financially sustainable and competitive, so that they can continue to serve their supporters and communities long into the future, no matter what level of the pyramid they play in.”

The EFL leadership has consistently said it wants a football-led solution to what it argues is a structural imbalance. But after two years without a resolution, it has become more willing to speak up in favour of a regulator taking on the challenge. The key to this, in the eyes of the EFL, is the backstop powers granted to the regulator in the event of no deal being agreed.

“The league eagerly anticipates the introduction of the football governance bill given it is now more important than ever that the independent regulator is provided necessary powers to secure the long-term sustainability of the pyramid,” the statement said.

After the Premier League’s decision to step back from a deal, reports have suggested that the government plans to expedite the rollout of the bill. On Thursday, however, there was still no agreed date for the first reading in the House of Commons and the shadow leader of the House, Lucy Powell, said Labour would make the introduction of a regulator “an election issue” in places with struggling clubs if the government did not act.

“If the Conservatives want to make this an election issue in those places, I say bring it on,” Powell said. “Let us be really clear: if they do not want to regulate football governance, then we will.”

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In reply, the Leader of the House, Penny Mordaunt, said: “When we bring legislation to the House, it will need to have the confidence of the English Football League, and, having attended many events with the EFL myself, I know that that is clear and understood.”