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 said the FA lacks independence and makes decisions based on vested interests due to a lack of checks and balances.
It also said the FA was resistant to change and that parliament needs to step in.
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.
"It may well move us to redressing the woeful lack of English players or managers and the embarrassing failures of our national team for the past 50 years."
