Wendy Alexander said yesterday that she had no plans to resign as Scots Labour leader after Gordon Brown failed to back her proposal for a referendum on Scottish independence.

Mr Brown's refusal during Prime Minister's Questions in the Commons to endorse her position appeared to undermine her and distance the Prime Minister from her leadership.

There were doubts in the party about how long Ms Alexander can carry on after Labour's policy on the constitution descended into chaos, and her credibility was questioned.

Mr Brown's failure to support Ms Alexander was all the more humiliating, coming just hours after she appeared on television claiming to have the Prime Minister's backing for her high-risk strategy of calling Alex Salmond's bluff over a public vote on separation.

David Cameron put Mr Brown under pressure to say whether he backed Ms Alexander. Asked by the Tory leader whether he agreed with her that there should be a referendum now, Mr Brown said: “It is not what she has said. The Conservative Party, the Liberal Party and the Labour Party have joined together to set up the Calman review, the commission on devolution, and I hope we can see progress on that commission and we will review that progress before we make any further decisions. And I thought that was the policy of the Conservative Party who supported the commission.”

Mr Cameron accused the Prime Minister of “losing touch with reality” before going on to quote Ms Alexander's comments from a television interview on Sunday.

“This is what Wendy Alexander said: ‘I don't fear the verdict of the Scottish people,' she told BBC Scotland on Sunday ‘Bring it on', what else could that possibly mean?”

The Prime Minister insisted that she was referring to the hollowness of the SNP who had promised an immediate referendum but would not now hold one until 2011.

Mr Brown's comments also contradicted Ms Alexander's claims on the BBC's Newsnight Scotland that he did support her. Interviewed on Tuesday night after she had outlined a proposal to bring forward her own referendum Bill at Holyrood in the event that the SNP did not produce theirs she was asked whether the Prime Minister was “endorsing it and he has told you that”. Ms Alexander replied: “Yes.”

Ms Alexander was attacked by opponents at Holyrood over her party's embarrassing predicament.

Nicola Sturgeon, the Deputy First Minister, said: “Wendy Alexander's position is now completely untenable. At a stroke, Gordon Brown has destroyed her leadership and placed serious questions over his own, given the number of inaccuracies in his PMQ answers.

“This is a disastrous Grand Old Duke of York double act - Wendy marches Labour to the top of the hill, and Gordon marches them down again. Labour must be in a parallel universe.”

Annabel Goldie, the Scottish Tory Leader, claimed that Mr Brown had delivered a masive vote of no confidence in Ms Alexander. “When asked whether he backed Wendy Alexander, Gordon Brown instead hung her out to dry. This is not leadership. It is a shambles.”

Nicol Stephen, leader of the Scottish Lib Dems, said: “It is clear that there is utter chaos at the top of the Labour Party. The Prime Minister has completely failed to support Wendy Alexander's call for an immediate referendum.

“This is very close to meltdown. Nobody knows what Labour stands for anymore and its leadership is in disarray,” he added.

Ms Alexander's aides attempted yesterday to portray an image of a united front between the Prime Minister and the Scottish Labour Leader. Her spokesman said: “Gordon Brown did not attempt to cut Wendy down - to say otherwise is nonsense.”

In a statement Ms Alexander said: “The Prime Minister and I are agreed about exposing the hollowness of the SNP's position, claiming they favour independence, yet wanting to hold a referendum in only 2010 or 2011.

“David Cameron is wrong. His question showed his continuing lack of understanding of the process. The Prime Minister was right to say no one was proposing a referendum at Westminster.

“The procedures of the Scottish Parliament mean that even if the SNP or anyone else introduced a Bill at Holyrood it could take up to 12 months to be considered.”

Ms Alexander's plan to bring forward a referendum Bill also suffered a setback at Holyrood.

The Scottish Parliament rules state that the lawmaking process cannot be started if the Holyrood government of the day plans its own legislation on the same proposal within the parliament's four-year term.

The prospect of Ms Alexander bringing forward her own Bill, a plan she had trumpeted on Tuesday, was last night being described by her aides as only an option.

The Calman Commission set up to investigate Holyrood's powers is due to produce an interim report this summer but will not publish its final report until 2009.

The SNP government is planning to introduce a referendum Bill in 2010 and to hold a referendum on independence later that year. The Nationalists believe that it is now impossible for Labour MSPs to vote against their Bill after the party's group voted to back a referendum earlier this week.

Times Recommends

• How I lost the gift of joy for a while
• Why Ann Widdecombe has got it wrong
• Alas, it’s the end of the road for petrolheads