David Bernstein, David Davies, Greg Dyke, Alex Horne and David Triesman grouped together to write to Damian Collins, chairman of the Culture, Media and Sport Committee.
They say the "well-meaning individuals" in charge of the FA are "collectively unrepresentative of English society" and "under-qualified" to deal with modern football.
The group also called for legislation to be passed, blaming the FA's "inability to reform and modernise in a fast-changing world".
The letter concluded: "Football is a much-loved sport enjoyed by millions, and it has genuine cultural significance in the country which first codified what is now a global sport.
"A focused intervention can undoubtedly build on these attributes, as has been recognised in many past inquiries and reports. It would give millions of players and fans confidence they will no longer be marginal to the future of their sport.
Responding to the letter, Collins wrote: "The select committee shares your concern that the current structure of the FA makes it impossible for it to reform itself.
"As such, there is currently no effective governing body for football in England that is capable of responding to the challenges that face the modern game."
Collins said the committee is working to prepare a draft Bill which would reform the structure of the FA.
"We cannot afford to wait any longer," he said.
A statement from the FA in response to the letter to Collins read: "The FA is currently working on governance reforms to adhere to Sport England and UK Sport's Governance Code for Sport which was released in October this year.
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