Campaigners lobbied MPs ahead of the Commons vote
Some 88% of the British public want a referendum on the EU's Lisbon Treaty, according to private polls for the I Want a Referendum (IWAR) campaign.
The unofficial ballot was conducted by postal vote last month in 10 Labour and Liberal Democrat marginal seats.
A total of 152,520 people voted, with 133,251 backing a referendum. IWAR claims the turnout is higher than that in local council elections.
Higher education minister Bill Rammell dismissed the poll as "flawed".
IWAR sent 420,000 ballot papers to voters on the publicly-available part of the electoral roll, and says turnout was 36.2% of those on the register.
Constituencies where the mini-referendums were held included those of Home Secretary Jacqui Smith, Transport Secretary Ruth Kelly, Europe Minister Jim Murphy and Liberal Democrat home affairs spokesman Chris Huhne.
Mr Rammell said the turnout figure in his Harlow constituency where a vote was held was "lower than any local government election that I have ever participated in."
"There are some real questions to be answered by the organisers," he told BBC1's Politics Show.
"Why 10 Labour and Liberal Democrat marginal constituencies? Why not one referendum in (Tory former chancellor) Ken Clarke's constituency, who is arguing against a referendum?"
Derek Scott, former Downing Street aide and chairman of IWAR, said: "We have taken the most up-to-date and the only publicly-available register there is and on that basis it is a very substantial turnout.
"There is no reason to suppose that people who have not been sent ballot papers... would be any different.
"There is a very significant number of people across the country who want a referendum."
IWAR is backed by Labour former ministers Kate Hoey and Frank Field and Lib Dem Mike Hancock, but has faced Labour accusations it is a Tory front rather than a genuinely cross-party organisation.
It says it only campaigned against Labour and Lib Dem MPs in marginal seats because both parties broke their pledge to hold a referendum.
The poll was carried out by Electoral Reform Services, a firm of independent election scrutineers recognised by the government and the UN.
Respondents were asked whether the UK should hold a referendum on the Lisbon Treaty, with 88% voting 'yes'. They were also asked if the UK should approve the treaty and 89% voted against.
The result comes ahead of a Commons vote on Wednesday on a Conservative amendment to the EU Treaty Bill, calling for a referendum.
The Lisbon Treaty, also known as the EU Reform Treaty, was drawn up to replace the EU Constitution, which was abandoned in 2005 after being rejected by Dutch and French voters.
Ministers say it only amends the EU's existing treaties and a referendum is therefore no longer needed.
But the Tories, UKIP, SNP, Plaid Cymru, DUP and various groups, including IWAR, say the treaty and the axed constitution are substantially the same and that the public must have a say.
Some Labour and Liberal Democrat MPs also back a public vote. The Lib Dem leadership wants a referendum on the wider question of Britain's membership of the EU.
Welcoming the result, Ms Hoey said: "All MPs should now take note, listen to their constituents and vote for a referendum on Wednesday."
Nigel Farage, leader of the UK Independence Party said: "If Parliament continues to ignore the wishes of the people, as shown by these votes in just 10 constituencies, it becomes clear that to remain legitimate the Government must grant us a poll in all 646 constituencies."