Labour have confirmed they will not contest the by-election forced by the ex-shadow home secretary David Davis.
The announcement came moments after Mr Davis formally resigned as an MP.
Mr Davis announced last week he was to force a by-election in his Haltemprice and Howden seat, which he intends to fight on the issue of civil liberties.
Mr Davis said that if Gordon Brown did not put up a candidate "people will see him as gutless". The prime minister has called the by-election a "farce".
At prime minister's questions, Mr Brown taunted Conservative leader David Cameron, asking if Mr Davis would be listed on the by-election ballot paper as a member of "David Cameron's Conservatives".
Labour deputy leader Harriet Harman earlier accused Mr Davis of "wasting over £80,000 to run a by-election, paid for by the council taxpayers".
She defended Labour's decision not to put up a candidate. "By-elections are for when a member of Parliament dies or when they are genuinely going on to another job," she told the BBC.
We will have the debate, even if Mr Gordon Brown, who is my real opponent in this, stays in hiding in Downing Street
"This by-election is a frolic and it's more to do with internal divisions in the Conservative Party."
But announcing his resignation on the steps of the Treasury, Mr Davis accused Labour of running away from a debate on their anti-terror legislation.
"There is no doubt in my mind this is the right thing to do. I have never been so sure of a principle in my life," he told reporters.
He said the public were on his side and he confirmed he would be standing as an official Conservative candidate.
"We will have the debate, even if Mr Gordon Brown, who is my real opponent in this, stays in hiding in Downing Street."
He added: "Mr Brown likes to talk about Britishness - fundamental to Britishness is being free. He should come out and argue the case."
Mr Davis announced he would be stepping down as an MP and shadow home secretary on Thursday - the day after the House of Commons voted by a narrow margin to extend the maximum time terrorism suspects can be held, before they are charged, from four to six weeks.
The proposal passed through the Commons by a margin of nine votes, against the opposition of the Tories, Lib Dems and 36 Labour MPs.
His resignation, apparently against the wishes of party leader David Cameron, took politicians by surprise.
The Liberal Democrats and British National Party have both said they would not be standing in the poll, likely to be held on 10 July.
The Official Monster Raving Loony Party is expected to field a candidate and several other fringe candidates have also expressed an interest.
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