Andy Burnham, one of the favourites to be next Labour leader, has issued a surprise call for David Cameron to bring forward his plans for an EU referendum.

Labour has consistently argued against holding a referendum, but after Ukip received four million votes in the general election campaigning on an anti-EU basis, Mr Burnham has now conceded that there is “clearly an appetite” for a vote on Britain’s membership of the bloc.

Mr Burnham insisted that he remained staunchly pro-European and that he would want to make that case to voters, but demanded a referendum be held by next year in order to avoid “a prolonged period of uncertainty and argument”.

During an interview with the BBC’s Andrew Marr Show, the MP for Leigh in Greater Manchester announced that he had received the backing of the influential shadow work and pensions secretary Rachel Reeves for his campaign to become leader – a former supporter of Chuka Umunna, who has withdrawn his own bid for the party leadership.

And Mr Burnham, who was the chief secretary to the Treasury in 2007-8, admitted to Andrew Marr that the party should have taken more care of the public finances when in government.

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Unite boss Len McCluskey has previously declared his support for Mr Burnham as a possible Labour leader, but the MP denied that he was the traditional “union candidate”.

“I’m the unifying candidate,” Mr Burnham said. “I am the change candidate, because we have got to reach out to those voters who had doubts about us on immigration and economic competence.”

On his new support for a referendum as soon as possible, Mr Burnham said: “I have been watching how public opinion has been changing. There is clearly an appetite for (an EU) referendum.

“That is why I am the change candidate in this election. I have said very clearly and quickly that we need to bring forward that referendum, because the worst of all worlds is a prolonged period of uncertainty and argument.”

Mr Burnham suggested he would argue the case for staying in the EU regardless of whether the Prime Minister could secure a renegotiation of immigration rules.

But he warned that “we will only be able to win that argument if we have a credible package of reforms”.