The Sunday Times reported today that a cache of documents which exposed that Qatar's victory in securing the tournament was sealed by a covert campaign by disgraced former football official Mohamed bin Hammam.
The report said the former Qatari vice president of Fifa, world football's governing body, used secret slush funds to make dozens of payments totalling more than five million dollars to senior football officials to create a groundswell of support for Qatar's bid.
It said he used 10 slush funds controlled by his private company and cash handouts to make dozens of payments of up to 200,000 dollars (£120,000) into accounts controlled by the presidents of African football associations who held sway over how the continent's four executive members would vote.
Shadow International Development Secretary Jim Murphy called for the decision to be "cancelled and re-run" if the allegations were found to be true.
He told BBC Radio 5 Live's Pienaar's Politics: "I think the Qatar decision has always been controversial of course, but sometimes it was seen by the Qataris as sour grapes from the English or others across Britain. But if these allegations turn out to be true there can be no question about this.
"The thing wasn't done fairly, it wasn't done openly and it would have to be cancelled and re-run entirely. The building that is happening in Qatar should be paused and they should have a fair and open competition. The failure to do so would amount to the biggest crisis in Fifa since its formation in 1904."
John Whittingdale, chairman of the Commons Culture, Media and Sport select committee, said: "My committee examined allegations two years ago that there had been corrupt payments involved in the decision, and we called for a full, transparent investigation. However, since then, Fifa have attempted to brush off the allegations and not taken them anything like sufficiently seriously.
"If these revelations prove to be correct they are obviously extremely serious.
"There does need to be an urgent and full transparent investigation to establish the facts."
Mr Whittingdale said Fifa president Sepp Blatter's position was "almost untenable" as he had been very dismissive of the allegations over the past couple of years and did not appear to have taken them seriously.
"There have already been serious doubts raised about the capability of Qatar to host the 2022 World Cup on football grounds. If the choice of Qatar was as a result of improper payments being made, then that strengthens an already strong case for re-running the whole 2022 contest."
Today's report said the official Qatar bid committee had always insisted Bin Hammam was an entirely separate individual who had nothing to do with the campaign to take the World Cup to Doha.
It said the bid committee was quick to disown him when he was banned from world football in 2011 after being caught bribing voters in his campaign to be elected Fifa president.
But the leaked documents show how he worked with the leaders of the bid and lobbied key voters, arranging lavish junkets paid for by the 2022 team at which he offered football officials large payments in exchange for their support, the newspaper said.
Fifa vice-president Jim Boyce said he would be in favour of re-running the vote if allegations that widespread corruption was involved in the bid were proved.
Boyce, who was not on the executive committee of the world governing body at the time of the vote, said Fifa's chief investigator Michael Garcia, who is already looking into allegations of corruption, would have to widen his investigation.
Boyce told Radio 5 Live's Sportsweek programme: "As a member currently of the Fifa executive committee, we feel that any evidence whatsoever that people involved were bribed to do a certain vote, all that evidence should go to Michael Garcia, whom Fifa have given full authority to, and let's await the report that comes back from Garcia.
"If Garcia's report comes up and his recommendations are that wrongdoing happened for that vote for the 2022 World Cup, I certainly as a member of the executive committee would have absolutely no problem whatsoever if the recommendation was for a re-vote.
"If Garcia comes up with concrete evidence and concrete evidence is given to the executive committee and to Fifa then it has to be looked at very seriously at that time, there's no doubt about that."
Minister for Defence Personnel, Welfare and Veterans, Anna Soubry said: "Somebody somewhere has got to get a serious grip on Fifa about the way that they run these competitions."
Asked on BBC One's The Andrew Marr Show if fellow ministers in the Cabinet would be looking at this, she replied "undoubtedly", adding Sports Minister Helen Grant "will also be wanting to look at this as well".
Gerry Sutcliffe was sports minister during the bidding process for the 2018 and 2022 World Cups, which were awarded simultaneously. England bid for the 2018 tournament, but lost out to Russia.
He cast doubt on whether a re-run of the 2022 bid would be possible, but said urgent action was required to show potential bidders for future tournaments it was still worthwhile funding a bid.
"It's called into question the whole integrity of Fifa," he said on Radio 5 Live.
"I think it would be difficult to re-run 2018 and 2022 now because the commitments have been made.
"What I think should happen is the FA, through Uefa, should make strong representations to Fifa, because what's going to happen is people are not going to bid in the future if it's not a fair and transparent process."
The committee which organised Qatar's successful bid has denied any wrongdoing
It said in a statement: "In regard to the latest allegations, we say again that Mohamed bin Hammam played no official or unofficial role in Qatar's 2022 Bid Committee. As was the case with every other member of Fifa's executive committee, our bid team had to convince Mr bin Hammam of the merits of our bid."
It said it was cooperating fully with the ongoing investigation of Fifa's Michael Garcia and remained totally confident that any objective inquiry would conclude it won the bid to host the World Cup fairly.
It added: "Following today's newspaper articles, we vehemently deny all allegations of wrongdoing. We will take whatever steps are necessary to defend the integrity of Qatar's bid and our lawyers are looking into this matter.
"The right to host the tournament was won because it was the best bid and because it is time for the Middle East to host its first Fifa World Cup."