The Football Association is "screaming out to be reformed", according to ex-FA executive director David Davies.
Davies' comments came after Sam Allardyce left the England job due to allegations that he offered advice on how to circumvent rules on transfers.
His view was supported by former FA chief executive David Bernstein, who said the FA "produce poor results".
"It is in need of serious reform and it isn't a coincidence these things keep happening," said Bernstein.
Allardyce parted ways with the FA just 67 days into his tenure, after the Daily Telegraph said he advised undercover reporters posing as businessmen on how to "get around" the FA's regulations on player transfers.
Meanwhile, the League Managers' Association says it is "extremely concerned" after the Telegraph also alleged that eight current or ex-Premier League managers have taken bribes related to player transfers.
"The sooner the allegations of corruption are dealt with by an independent commission the better, there's no doubt about that," Davies told BBC Sport.
"Let's have an independent enquiry, let's get all the allegations out there and let's assess them and let's see what evidence there is."
In July, sports minister Tracey Crouch warned that football could lose millions of pounds of funding if it didn't reform its governance.
"I'm not shy to say to the FA 'if you don't reform your governance structures, I will give that money to other bodies that deliver football'," she told BBC Radio 5 live.
Crouch said there was good work being carried out by association executives but problems revolved around the FA Council, which has 124 elected members.
Another to call for reform within the FA was former chairman Greg Dyke, although he admitted it may not have made any difference "in these circumstances".
"Whether the FA needs to be a much tougher regulator is worth a debate," he told BBC Radio 5 live.
"In most of the jobs that I've ever done, you look at what needs to be done and you do it. At the FA we knew what needed to be done but doing it was very difficult."
What next for the FA?
After just one match in charge - a 1-0 win over Slovakia in England's opening game of their World Cup 2018 qualifying campaign - Allardyce becomes the national side's shortest-serving full-time manager.
The FA said it would begin its search for a new England manager, while under-21s boss Gareth Southgate takes charge for the Malta game as well as World Cup qualifiers against Slovenia and Scotland plus a friendly with Spain.
Allardyce was due to name his next squad on Sunday.
However, while Davies said that it was "entirely true" that the image of English football has "suffered", he claimed that defeat to Iceland in the last 16 of this summer's European Championships was "the lowest moment".
"I've known senses of doom before and they do pass," he said.
"There will be a new manager and, God willing, that manager will take England to the next World Cup - and who knows what the future holds on the pitch?
"Let's give that manager and, most importantly, the players the best chance to be successful by the way the game is governed off the pitch."