Just a month after the issue caused a rift with Gordon Brown, the Scots Labour leader told an audience on Radio 4's Any Questions that "we're going to have a referendum". She then called on First Minister Alex Salmond to "get on with it" by bringing forward the date of the referendum from 2010 – the date he has currently set.

Alexander's spokesman last night insisted that she was merely restating her position. But her declaration that the referendum is "going" to happen prompted claims by the SNP that Alexander had now guaranteed her support for a vote – and prompted further warnings that the strategy has not been backed by the Prime Minister.

Alexander was addressing the question during a round-table debate on the BBC's flagship politics programme.

"I don't think it is in Scotland's interests to have this continuing uncertainty. We're going to have a referendum – get on – let the people of Scotland speak," she said. "Ultimately, whether you remain part of the sovereign state is a matter for the people."

In a message to Salmond, she added: "We shouldn't be leaving it until the last few months (of the Scottish Parliament's four-year term] – get on with it."

Alexander has told friends her support is aimed at preventing Salmond from being able to accuse Labour of preventing Scots from having their say on independence. She feared that, had Labour continued to oppose the vote, Salmond would have used their position to gain further support for the SNP in the 2011 Scottish elections.

But the policy does not have the backing of large sections of the party. One insider said last night: "There is a sense of frustration when she does this because it is bad for her more than anyone else. She should stop shooting herself in the foot, assuming she has any feet left. The Labour Party can't decide on this without putting it to the membership."

Another critic said: "There is still a hope that she will go sooner rather than later, and this will just add to that feeling. We need a professional leader in charge, and she isn't it."

Alexander's latest comments received a cool response from Downing Street yesterday. "This is a matter for Wendy Alexander. There is nothing new in these latest comments," said a spokesman.

Previously, enterprise spokesman Iain Gray had ruled out Labour voting for the SNP's current bill as it stands unless the wording of the proposed referendum question is changed. Under the SNP's proposals, voters would be asked to agree or disagree that "the Scottish Government should negotiate a settlement with the government of the UK so that Scotland becomes an independent state".

A spokesman for Alexander said: "They will not vote for any question, but the principle remains – that Labour believes that the Scottish people should have the opportunity to decide on the question of whether the country becomes a separate state, with a fair question put to them. Her position has not changed on that."

However, the SNP insisted last night that Alexander's comments locked her in to backing a referendum bill.

SNP MSP Kenny Gibson said: "By reviving her call for an independence referendum, Wendy Alexander has backed Labour into a constitutional corner – while also exposing how the party is disintegrating in Scotland and across the UK. In Scotland, she has left Labour with no real choice but to back the Scottish Government's planned referendum bill in 2010."