All week the corporation has been receiving complaints from viewers about the absence from the 10-strong shortlist of Walliams, 35, who made the crossing in a remarkable 10Å hours.

In a year of sporting disappointment, some have alleged that the BBC has rigged the voting process to avoid a potentially embarrassing victory for the actor known for his transvestite sketches and catchphrase “I’m a laydee”. Past winners include the late Bobby Moore, Sir Steve Redgrave and Ian Botham.

Tonight’s favourites for the award are Zara Phillips, 25, daughter of the Princess Royal, who won the three-day event world championship in Germany this summer, and Darren Clarke, 38, the golfer who helped Europe to win the Ryder Cup six weeks after his wife died of cancer. Should Phillips win she would be following in the footsteps of her mother who won the title in 1971 as European three-day event champion.

Millions of people are expected to vote for the 10 nominees on the shortlist by telephone or text tonight. The Sport Relief charity will receive 12p from the cost of each call and 8p from each text.

Fan websites for Little Britain encouraged people to nominate Walliams for the prize and at one stage he was the odds-on favourite with bookmakers to win after raising £1m from the swim for Sport Relief. Even the current issue of Radio Times includes him as one of the “names in the frame” in contention for the title.

However, when the shortlist was announced last week Walliams’s name was missing. Instead Phil “the Power” Taylor, the darts player, was said to have received more nominations.

The voting for the shortlist was structured to avoid a straight popular vote. Newspaper sports editors and a BBC panel of experts led by Gary Lineker, Sue Barker and Adrian Chiles, the presenters of tonight’s show, were asked to nominate their own top 10.

Each of their votes carried as much weight as the collective online verdict of the public. It meant the opinion of the sports editor of the Coventry Tele-graph had as much influence as almost 200,000 online voters.

Two newspapers, The Sun and London’s Evening Standard, nominated Walliams. The Daily Record in Scotland even proposed Sven-Goran Eriksson, England’s much-derided former football coach.

One insider at BBC Sport said: “Officially all votes were of equal weight but they weren’t going to have the likes of Walliams, Eriksson, or even Graham Poll [the referee who bungled in the World Cup by giving the same player three yellow cards].”

Previous awards have been plagued by accusations of a BBC fix. Eleven years ago it ducked a campaign by Britain’s 3.2m anglers to nominate Bob Nudd, a world fishing champion. Last year it sidestepped an organised attempt by Everton fans to select Peter Crouch, then a luckless forward who had yet to score for Liverpool, their arch rivals.

Viewers have claimed that if it had been left to the public vote Walliams was a certainty to be on the shortlist. Last month he was voted winner of the Pride of Britain award for the most influential public figure in recognition of his swim. He trained for a year and his time was the 23rd fastest out of 1,200 crossings.

One viewer, Peter Field, said on the BBC sports editors’ blog: “For a non-professional, David Walliams did his swim in some kind of record time. He and Jane Tomlinson [the charity cyclist who suffers from cancer] dilute the braggadocio that professional sport has given us of late.”

The BBC denied there was a ploy to remove the comic from the list of contenders. “David Walliams was entitled to be nominated under our criteria,” it said.

“The method of voting was the fairest way of doing the nominations in order to get a fair representation of sports experts as well as the general public, and to avoid the ongoing problem of block voting campaigns.”

The BBC refused to release the voting figures but claimed that even on popular votes, Walliams was 800 behind Taylor, the world darts champion, who came 10th. However, Walliams has now been invited on to the show and is expected to receive a special award.

Walliams declined to comment on the controversy but said he was planning another charity swim. His spokeswoman said he was looking at several options, including the possibility of swimming from Russia to America across the Bering Strait.

Yesterday, in another surprise decision, the BBC announced that the Arsenal player Theo Walcott, 17, who went to the World Cup but never kicked a ball, had won the young sports personality of the year award.

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