A summit meeting of the 24 Championship clubs will on Wednesday warn the Premier League that it risks permanently damaging the "integrity of the Football League" by proposing a big hike in parachute money for clubs relegated from the top tier but only a modest rise in "solidarity payments" for other clubs. Furious chairmen have said they could ultimately turn their backs on the Premier League in protest, while others believe that their recently introduced financial fair play rules will become "completely unworkable" if the scheme goes ahead as planned.

With the Premier League close to finalising a record £5.5bn windfall in broadcasting income, MPs have also warned of this being soaked up by a "culture of greed" at the top of the game and called for the money to be shared more widely to benefit the grassroots and fans' organisations.

The blockbuster TV deal, fuelled by the emergence of BT as a rival to BSkyB for domestic live rights and the continued growth of overseas income, has reignited a fierce debate across football and Westminster about how the cash should be shared and how far the Premier League's responsibilities to the wider game should go. Some MPs have called for a minimum of 7.5% of the total income to be distributed to the grassroots, while others have called for a new funding formula that disaggregates the distribution of cash from the three-year cycle of TV deals to provide greater certainty.

Many of the organisations funded through the Premier League's TV income, such as the Football Foundation, Supporters Direct and Kick It Out, are nervously awaiting the outcome of the next Premier League meeting in mid-April to discover if it will translate into increased funding.

The Premier League, which will this week launch its Creating Chances annual review demonstrating how its distribution of the money flowing into the game from broadcasters is helping grassroots projects, will argue that it gives away more money than any other League.

Football League chairmen will try and persuade those clubs already in receipt of parachute payments to support a plan to recalibrate the offer so that the total is shared more equally, but it is understood that the Premier League is unlikely to unpick the deal. At their April meeting, Premier League clubs will discuss proposals that £62.7m should be split between the Football League clubs, but under the plans £69m will go to the three relegated teams alone in their first season back in the Championship.

As described in a letter to Football League clubs by the chairman, Greg Clarke, relegated clubs will receive £23m in the first year (a £7m increase), £18m in the second (£5m) and £9m in years three and four. Clubs in the Championship who do not get parachute payments currently receive £2.3m a season, League One sides £325,000 and League Two sides £250,000. It is proposed that those payments are increased by around 5% under the new offer.

"If you're getting £2.3m a year and your rivals are getting £23m, how is that sustainable? How do you compete? It also makes it very difficult to see how financial fair play can be sustained," said one Championship source.

The Premier League will argue that the parachute payments are governed by a formula contained in its Founder Members Agreement while the solidarity payments, a more recent concept, are covered by a separate negotiation. Its executives will also argue that the solidarity payments are only one part of a wider package of assistance, including money towards youth development, community projects and a slice of the £320m invested in the Elite Player Performance Plan over the next four years that is designed to revolutionise the academy system.

They can also point to the fact that only one club in the current top six of the Championship is currently in receipt of parachute money (Hull City) and that last season only one of the three promoted clubs had received parachute payments (West Ham). But the Football League clubs say that there is not enough data to yet judge the effect of the discrepancy.

The Premier League will also face renewed accusations it is not spreading its £5.5bn broadcasting windfall widely enough. Fans' groups are campaigning for some of the extra cash to be used to subsidise ticket prices, while the Labour MPs David Crausby and Steve Rotheram have launched a campaign to raise the minimum contribution to grassroots football and "good causes" from around 4% to a guaranteed minimum of 7.5%.

The shadow sports minister, Clive Efford, told the Guardian clubs "can't continue to foster a culture of greed" and that there should be a commensurate increase in money for grassroots football "as an absolute minimum". "Communities that have supported football clubs for generations must benefit alongside the clubs themselves from this windfall," he said. "There is a very strong moral obligation on the Premier League to make sure grassroots sports benefit from this windfall.We want to see greater co-ordination between the major sports and minority sport."

John Whittingdale, the Tory MP who is the chairman of the culture, media and sport select committee that recently compiled a critical report on football governance, told the Guardian that the status quo was "unsustainable" and that more money needed to flow through the FA to the grassroots. "In our view, the FA needs to be much more clearly the body that governs the whole national game and we need to get back to reducing the power of the Premier League within it. If that is achieved, it will follow on that football as a whole benefits from the sale of broadcasting rights rather than just players and agents."