Pressure is building on the government ahead of this week's Commons vote on whether there should be a referendum on Europe, after a huge polling exercise across Britain showed overwhelming backing for the public's right to have a say.

Campaigners demanding a referendum on the controversial Lisbon Treaty, on the grounds that it is effectively a constitutional change, staged their referendum exercise in 10 marginal Labour and Liberal Democrat constituencies across the UK, including the East Renfrewshire seat of Europe Minister Jim Murphy.

The I Want a Referendum Campaign' (IWAR) sent out 420,791 ballot papers to all those on the latest publicly available section of the electoral roll. A total of 152,520 - 36% - were returned, of which 133,251 - 88% - were in favour of a referendum.

In East Renfrewshire, 31% of those who received ballot papers returned them, almost 21,000 people voted with 85% in favour of a referendum.

But Mr Murphy told the BBC Politics show yesterday: "It's clear that less than one in six people in East Renfrewshire voted for a referendum. The Conservative Party spent £50,000 so it was almost £5 for every person who returned a ballot paper."

The local campaign in the area was called East Renfrewshire EU Choice and its spokesman, Richard Cooke, insisted the Tories did not put up the money for the exercise.

He said he was "stunned to hear a government minister tell such outright lies", saying the Tories did not put in a single penny to the campaign and the figure for those in favour of a referendum was double what Mr Murphy claimed.

"The reality is that an overwhelming majority of people on a poll of this size have said they want a referendum and if they won't give us that then to reject this treaty."

Angus Robertson, leader of the SNP at Westminster, said last night: "This is a result for democracy. It clearly demonstrates that public opinion backs a referendum on the Lisbon Treaty. The SNP MPs will vote this week at Westminster for a referendum. This increases the pressure on the Labour government to let the people have their say."

Labour Euro-rebel Kate Hoey predicted that many Labour and LibDem MPs would be prepared to defy their party whips and vote for a referendum in the Commons on Wednesday.

IWAR campaign chairman Derek Scott, a former economic adviser to Tony Blair, called it "a magnificent turnout and a great result."

He said that Labour and the LibDems should now honour their election manifesto promises to hold a referendum on the EU constitution, which, campaigners say, is broadly the same as the new treaty.

Shadow Foreign Secretary William Hague said the results clearly showed the public support for a referendum. "Despite the attempts of the government to rubbish this exercise, and the absence of national publicity, the turnout of voters has been higher than in some European elections and well in line with local elections," he said.

"It is time for Gordon Brown and Nick Clegg to listen to the people and keep their promise, rather than continue with the giant act of dishonesty in which they are now engaged."