Former Football Association chairman Lord Triesman has urged England's World Cup 2018 bid team to "come clean" if they attempted any vote swaps.
A recent report compiled by FIFA investigator Michael Garcia cleared Qatar and Russia of any wrongdoing in their respective World Cup bids.
The 430-page dossier, which has still yet to be published in full, also accused the English Football Association of giving football's world governing body a bad image, while disregarding bidding rules to try to stage the 2018 World Cup.
Lord Triesman, who acted as chairman of the 2018 bid until 2010, told reporters: "FIFA needs root and branch reform. Its culture will not be changed by tweaking the processes. Culture is always stronger than process. Mr [Sepp] Blatter and the old school must go. His intention to run again is bad for sport.
"The Swiss government should be involved, the major sponsors should be involved and I believe the bids for the World Cup in 2018 and 2022 should be re-run.
"If England has anything to say about vote swapping that is not to its credit then let's come clean as well and not advocate for others what we are not prepared to do for ourselves."
The British government last month became the latest to increase the pressure on FIFA to publish the full findings of their report.
