His SNP group will propose the move at Thursday’s full meeting of the city council, which is due to debate three options – scrapping the scheme at an estimated cost of £740 million, building the tram line as far as Haymarket for £700m or taking it as far as St Andrew Square at a cost of £773m.
An Evening News survey published yesterday showed 78.6 per cent of people were opposed to continuing with the project at the latest price.
Councillor Cardownie said: “It’s time the people of Edinburgh had their say.”
The SNP’s coalition partners, the Liberal Democrats, are expected to vote for completing the tram route as far as St Andrew Square. Labour and Conservative groups were meeting today to decide their views amid signs both are likely to back stopping at Haymarket.
Cllr Cardownie said his group would call for a referendum that put all three options to the public.
He said: “We have now tried four times to have the project scrapped. It’s obvious other councillors are not prepared to listen to us, so perhaps they will be prepared to listen to the people of the city.
“The SNP group would promise to abide by the outcome of such a referendum. We would abide by what the people told us.
“The people of this city have never had an opportunity to express an opinion on this issue. It’s about time they had their say.”
The Scottish Government, which is providing £500m of the original £545m budget for the trams, has made clear it is sticking to its “not a penny more” stance despite the escalating cost of the project, leaving the city council to find some way of borrowing the extra cash and repaying it.
Cllr Cardownie said: “Up till now the vast majority of money spent on this project has been Scottish public money, but any shortfall will have to be budgeted for with Edinburgh council taxpayers’ money, so they should determine what happens to this project.
“I’m sure people in Edinburgh would welcome the chance to give their view.”
He said he hoped the cost of a referendum could be kept to a minimum, but added the expense of giving people a say would pale into insignificance in comparison with the sums now being talked about for carrying on with the project.
“It’s now got to the stage where all the options will mean extra expenditure for the city and the people should have their say. For too long they have been kept out of the equation.”
In February 2005, Edinburgh staged a referendum on the previous council administration’s controversial road toll scheme at a cost of £520,000.
Ballot papers were sent to 291,000 homes across the city, asking people to vote yes or no to the congestion charging plans, which would have seen motorists paying £2 to drive into the city.
The result was a massive 74 per cent “no” vote.
Cllr Cardownie also rejected the idea that a referendum would just mean a further delay in the tram scheme.
He said officials were planning to come back with a further report in August or September, so there would be space to organise a referendum.
Even if it took longer to prepare for a vote, he said it was more important for democracy to be seen to prevail.
“The trams were meant to be up and running by now, but the earliest we would now get them is 2014. After what the people of Edinburgh have had to put up with, I don’t think a month’s delay is too much to ask.”
Opposition parties on the council were reluctant to back the referendum idea.
Labour transport spokeswoman Lesley Hinds said there was a need for political leadership from the administration over the trams.
She said: “We need all parties working together to get us out of this and get some trust back into the council as a whole.”
Tory group leader Jeremy Balfour claimed it was too late for a referendum. He said: “We have got to get clarity on this project and get it under control.
“That’s not to say we have not made mistakes and got things wrong, but collectively we have got to solve the issues.
“We need leadership from the administration or, if not them, from political parties willing to be constructive.”
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