MPs have called for the ­Independent Regulator for Football to have the scope to reintroduce replays to the FA Cup, amend the parachute ­payment system and to enforce an effective financial settlement between the Premier League and the EFL, as they voted in favour of progressing the Football Governance Bill.

The second reading of the bill was approved without a vote after a debate in the House of Commons on Tuesday. MPs from all sides of the house spoke in favour of the bill, including Conservative MPs who said they had previously been opposed to regulation. A number of politicians, ­however, called on the government to go ­further in granting the regulator power to achieve financial stability for the football pyramid.

Announcing the bill to the house, the secretary of state for culture media and sport, Lucy Frazer, said it was focused specifically on ­improving financial regulation. “If we want English football to remain a global success story, we have to ensure our pyramid is financially sustainable,” she said. “I am proud to say that the Football Governance Bill will do exactly that.”

A number of MPs questioned the scope of the regulator’s remit, however, ­arguing parachute payments, for example, would sit outside the ­regulator’s ­concerns as the bill is drafted, but directly impact financial outcomes in the football pyramid. ­Others pointed to the ­secondary ­responsibility of the regulator to ­preserve aspects of ­footballing ­heritage, and argued that these ­considerations should give the regulator the right to intervene on the issue of Cup replays, which caused a furore last week when the FA and Premier League agreed a deal to get rid of them from next season’s competition.

A number of MPs also addressed the issue of the so-called “­backstop” power which would allow the ­regulator to intervene in the event that the EFL and Premier League remain unable to strike a deal on financial ­redistribution. Members noted that the current legislation stated the backstop could only be activated by a ­competition organiser, not by the regulator itself, and the regulator had been given no powers to devise a settlement it thought would be best suited to delivering financial stability.

The bill will now go to the ­committee stage where MPs can ­propose amendments to the text. The MP and former Liberal ­Democrat leader Tim Farron said he would ­propose an amendment that would reintroduce replays to the FA Cup and ensure that all member clubs must have a vote in “deciding the organisation and rules” of the tournament.