In the latest extraordinary twist to the referendum saga, MSPs at a meeting of members of the Scottish Parliament's Labour group yesterday ditched Ms Alexander's weekend pledge that the party would not stand in the way of a referendum bill, instead either voting for it or abstaining.
It also reversed the position outlined by Duncan McNeil, the group chairman, last week when he said the MSPs would "not vote down any referendum bill that comes before this parliament".
The latest U-turn left the party in an almost identical position to ten days ago, before Ms Alexander first said she would support a referendum.
It led the Tories to compare Labour's policy to an infamous storyline in the TV soap Dallas, in which the death of a leading character was explained away as a dream.
Outlining the MSPs' new position, Mr McNeil said it was impossible to make any commitment to a bill which would not be introduced for another two years as the SNP did not want to put forward a referendum bill until 2010.
He confirmed that, contrary to suggestions made last week, Labour would not try to force the SNP's hand to bring forward a referendum bill early.
Mr McNeil added: "We reserve the right to scrutinise any bill that comes before this parliament."
A spokesman for Ms Alexander later said: "It all depends on the wording and the timescale of the bill."
And he insisted that Labour still supported a referendum on independence "in principle".
The Scotsman understands that the latest change of position came because many Labour MSPs were worried by a position which they saw as a blank cheque for the SNP, although Ms Alexander has always insisted she was not offering one to the Nationalists.
She had also told Labour MSPs last Tuesday that she had the support of the Prime Minister, an assertion she repeated in a television interview, but one which Mr Brown made clear was untrue in the Commons last Wednesday during Prime Minister's Questions.
Labour MSPs who are opposed to any referendum have now won a position allowing the party to vote against one, which is now the most likely outcome.
The latest shift was last night welcomed at Westminster, where Labour ministers had been holding their heads in despair at the issue.
A senior Westminster source said: "This is a huge relief. We haven't leaned on the MSPs to come to this position, they seem to have come to their senses by themselves.
"This is a much more sensible position than the one held before."
Malcolm Chisholm MSP, who was yesterday named the group's constitutional affairs spokesman, last night moved to defend the party's new position.
He said: "The SNP have turned down the chance to end the uncertainty facing Scotland and now will be at the mercy of Labour's parliamentary tactics."
However, David McLetchie, the chief whip of the Scottish Conservatives, was quick to compare Labour's latest moves to the much-maligned Dallas plot.
He said: "Whereas Pam woke up to find Bobby was still alive, the same cannot now be said of Scottish Labour as a credible opposition in this parliament."
Nicola Sturgeon, the deputy First Minister, added:
"Wendy Alexander has been utterly humiliated by the Labour group, who have effectively U-turned on her farcical U-turn. 'Bring it on' has been brought down, and Labour must now be very close to bringing Wendy Alexander down as their Holyrood leader.
"Her position is now impossible and completely untenable."
Nicol Stephen, leader of the Scottish Lib Dems, admitted he was bewildered by Labour's latest move.
He added: "Anyone trying to keep pace with Labour's ever-changing position would be driven to dizziness."