Barry Hearn has resigned as Leyton Orient's honorary president with the club having still not paid staff their wages for March.
His resignation comes as the EFL said it was "exceptionally concerned" about the situation at the club.
The EFL said it had sought answers from the owners without success. "Silence is not an acceptable response," it added.
Orient were relegated from League Two on Saturday with a 3-0 defeat at Crewe after 112 years in the Football League.
Owner Francesco Becchetti has been given until 12 June to sell the club or pay off his debts to creditors.
Hearn told BBC Radio 5 live his decision to quit was "not a statement that's anti-club, it's a statement that's anti-owner".
"I'm not prepared to put up with this sort of thing at a club my name is associated with," he added.
"The moment that owner is no longer there it's a different question and I'm available to help wherever I can."
Hearn ruled himself out of buying back the club, having been their chairman for 19 years.
He admitted his sale to Becchetti had gone "rather pear-shaped", having sold to the Italian on the promise that funds would be injected into the club.
But Hearn added: "What I didn't know is that he would spend it so badly and his management would be so appallingly bad."
'Staff forced to relocate'
Orient's employees are due to be paid their wages for April in four days' time, but they have yet to receive their wages for last month.
On 19 April, a statement from staff said they were "hugely concerned" by the "lack of communication" from the club's hierarchy.
Since then, staff say they have been met with "a wall of silence" in response to their request.
"We are extremely concerned about the ongoing situation given the effect of non-payment of mortgages and rent are already resulting in staff having to relocate," a statement said.
"Due to this we appeal to the English Football League and the Football Association to intervene on our behalf as the regulatory bodies in the sport and demand substantive answers from the club's board."
The FA said reports that club staff have not been paid were "very concerning".
EFL to offer help despite relegation
In its statement, the EFL said it last met with Leyton Orient's chief executive, Alessandro Angelieri, on 9 March.
"At this meeting, we received confirmation that funds would be made available to dismiss the winding-up petition and fund the club going forward," it said.
"The EFL board received an update on the situation at its meeting on 6 April with the club being asked to provide a further commitment following widespread reporting that the required funding had not been made available.
"No response has been received to date."
The EFL added that it would "continue to do everything it can to ensure that the future of the club is secured" despite their relegation to the National League.
The governing body is also working with club staff to ensure "appropriate arrangements" are in place for Saturday's final home game of the season against Colchester, and has arranged a meeting with the Leyton Orient Fans' Trust.
Troubles had 'big effect' on squad
Orient have had five different managers this season, but the changes failed to result in an upturn in form.
The O's have increasingly been forced to rely on their younger players, with seven teenagers included in the starting line-up in the loss to Crewe.
"It's a disappointing time when you're not being paid. Some people deal with it in different ways," manager Omer Riza told BBC Radio London.
"It's just unsettled everybody. People can't focus on their jobs properly and it's been tough.
"The whole season's been a big factor with what's gone on, but the boys in the last few performances have got out on the pitch and put in some good performances."