Senior Fifa figures are for the first time seriously considering the ramifications of ordering a rerun of the vote for the right to stage the 2022 World Cup, in the aftermath of new corruption allegations against the hosts, Qatar.

While awaiting the results of a semi-independent inquiry into the 2018 and 2022 bidding races, senior football figures heading for the 2014 tournament in Brazil are understood to be considering their response if the report recommends a new vote in light of new claims based on hundreds of millions of leaked emails and documents.

The Qatari organising committee for the 2022 World Cup is to meet Fifa investigator Michael Garcia on Monday in Oman, the BBC reports.

In Britain, there was a renewed outpouring of concern from politicians and former football executives after the Sunday Times alleged that Mohamed bin Hammam, a Qatari former Fifa executive committee member, paid $5m (£3m) in cash, gifts and legal fees to senior football officials to help build a consensus of support behind the bid.

The UK government, humiliated over England's own bid for the 2018 tournament, which garnered just a single external vote, has previously said the corruption allegations are a matter for Fifa.

But the sports minister, Helen Grant, signalled a shift, saying: "These appear to be very serious allegations. It is essential that major sporting events are awarded in an open, fair and transparent manner."

The shadow sports minister, Clive Efford, called for a rerun of the vote, in which Qatar overcame rival bids from the US, Australia, Japan and South Korea.

"This issue calls the governance of football into question. No one will have any confidence in a Fifa investigation run by Sepp Blatter," he said.

"Fifa must take urgent action and reopen the bidding for the 2022 World Cup if it wants to restore its credibility."

Writing in the Guardian, the shadow international development secretary, Jim Murphy, added: "Fifa's rules are clear – the World Cup hosting must not be bought."

Mohamed bin Hammam is at the centre of corruption allegations. Photograph: Mohamad Dabbouss/Reuters

John Whittingdale, the Tory chair of the culture media and sport select committee, said Blatter's position was "almost untenable" and called for a "urgent and full transparent investigation to establish the facts".

Fifa, gathering in São Paulo for its annual congress before a 2014 World Cup that has had a troubled buildup amid anger from Brazilians at the cost and corruption, referred inquiries to the office of Michael Garcia.

The former US attorney in New York is conducting a supposedly independent ongoing investigation into the bidding processes for the 2018 and 2022 tournaments.

He is expected to pass his conclusions to the adjudicatory chamber of Fifa's revamped ethics committee later this year. Meanwhile, the FBI is also conducting an ongoing investigation into payments to former Fifa officials.

Jim Boyce, the British Fifa vice-president, said he would have "absolutely no problem" if the ethics committee recommended a new vote in light of proven wrongdoing.

The Qatar 2022 organising committee claims that Bin Hammam, who was banned from football after bribing officials in a 2011 bid to unseat Sepp Blatter as Fifa president, had nothing to do with their bid.

Disgraced former Fifa vice-president Jack Warner is alleged to have been paid $1.6m. He has always denied any wrongdoing. Photograph: Jam Media/LatinContent/Getty Images

The Sunday Times said it had obtained a cache of hundreds of millions of documents and emails, which detailed conversations about payments and money transfers from accounts controlled by Bin Hammam, his family and Doha-based businesses. Among many other alleged payments to mid-ranking football officials and figures including the former footballer of the year George Weah, Bin Hammam paid a total of $1.6m to the disgraced former Fifa vice-president, Jack Warner, including $450,000 before the vote. Warner has always denied any wrongdoing.

He also allegedly paid $415,000 towards the legal fees of Reynald Temarii, the Fifa vice-president banned from voting in the original election following an earlier Sunday Times investigation. The legal process helped delay Temarii's replacement on the executive committee by his deputy, reducing the number of voting members to 22 and depriving Australia, one of Qatar's rivals, of a vote.

Qatar 2022 is likely to seek to argue that Bin Hammam was acting to further his presidential ambitions rather than on behalf of the World Cup bid. In a statement on Sunday it said he played "no official or unofficial role" in its bid.

"We are cooperating fully with Mr Garcia's ongoing investigation and remain totally confident that any objective enquiry will conclude we won the bid to host the 2022 Fifa World Cup fairly," said the organisers, who are consulting lawyers.

"We vehemently deny all allegations of wrongdoing. 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."

But the newspaper said the email trails proved Bin Hammam was in fact intimately involved with the audacious two-year campaign to bring the World Cup to the tiny oil and gas-rich Gulf state, where temperatures can top 50 degrees in June.

In November 2010, the World Football Insider website quoted the bid chairman, Sheikh Mohammed bin Hamad bin Khalifa Al-Thani, as saying Bin Hammam was the campaign's "biggest asset" and had been a crucial mentor for his team.

One obstacle surrounding a potential re-vote, apart from a likely legal challenge from Qatar, would be the difficulty in re-running the 2022 vote without also reopening the 2018 process. Russia won the right to host the 2018 World Cup in an ill-defined dual process riddled with controversy.

Despite promising his current term would be his last – and the ongoing travails of the organisation with which he is inextricably linked – Blatter, who last month called the choice of Qatar "a mistake", has vowed to stand again for the Fifa presidency in 2015.

• Qatar World Cup: Bin Hammam 'acted like head of crime organisation'