The century-long dream of electoral reform in Britain looks likely to be dashed for more than a generation, with a Guardian/ICM poll predicting that voters will back keeping first past the post by a crushing majority.

The survey, before the referendum on whether to introduce the alternative vote (AV) for elections to the Commons, predicts a 68% no vote with just 32% for yes. The hopes of yes campaigners that there was going to be a late tightening of the polls have been dashed.

The findings suggest support for electoral change has slumped since a Guardian/ICM poll last month revealed the growing size of the no lead – then 16 points, now 36. In a Guardian/ICM poll in February, the yes campaign was two points ahead.

A YouGov poll for The Sun also predicts defeat for AV, showing 40% would vote yes, and 60% no. Only 25% of voters in that poll knew which way Eddie Izzard, the Yes campaign's most high-profile celebrity backer, intended to vote.

The referendum result, due to be formally announced on Friday, will prompt deep soul-searching inside the Liberal Democrats, and bitter recriminations over the way that David Cameron sanctioned a full-scale assault on Nick Clegg by the no campaign as a central part of its appeal.

Some in the all-party yes camp blame Clegg for abandoning a pledge to stay out of the campaign, saying his presence destroyed their appeal for a new kind of politics and meant their campaign was seen through the prism of the coalition.

Clegg vowed that the coalition would continue, but accepted the temperature has been rising inside his own party over the all-party no campaign's tactics. Refusing to concede defeat, he made a final desperate appeal for the yes vote saying: "If you basically think the current system is absolutely fine, totally perfect, nothing wrong with it then obviously vote no and stick with what we've got. If you want something a bit fairer, a bit better, which makes all politicians work a bit harder for your vote then vote yes, vote for change."

The Lib Dems fear they are likely to be hammered in elections for the Scottish parliament and Welsh assembly. They are also expected to lose more than 300 councillors in England – and fear as many as 600 losses – ceding control of almost every council they are defending.

There is no sign that any serious figure will mount a challenge to Clegg's leadership, but there will be calls for the party to adopt a cooler relationship with its coalition partners. Senior party figures privately admit that it may take as long as two years for the party to start to recover its former popularity.

Labour tried to play down expectations that it could win as many as 1,300 seats in the English council elections, saying that on the basis of council byelection results since the 2010 election the party is likely to win between 400 and 600 seats. Labour officials warn that in the south any collapse in the Lib Dem vote may see the Conservatives gain seats.

Independent experts have predicted Labour should make as many as 1,000 gains, and it is hoping to win Clegg's home city council of Sheffield, as well as Leeds, North Tyneside, Bolton, and Barrow in Furness.

Labour is worried that it is likely to fare much worse in Scotland than it expected three months ago, however, even though it has pulled back some support from the Scottish National party. In Wales Labour is on the brink of being able to form a majority government.

Ed Miliband, the Labour leader, is hoping that the expected crushing defeat for the advocates of the alternative vote will not rebound on him personally even though he has increasingly vocally supported the reform. He signalled that even if the vote is close no political party will return to the issue for a long time.

According to the Guardian/ICM poll, a majority of Labour supporters now say they will vote against AV despite Miliband's endorsement of change. So will almost nine in 10 Conservatives and more than a quarter of definite Lib Dem voters, whose lukewarm support seems confirmed by the fact that they are now less likely than Conservative or Labour voters to say they will turn out. Young voters remain in favour of AV, but are the least likely to vote.

Among all voters, before adjustment for likely turnout, 28% said they were for change, with 52% against and 20% who said they didn't know. After adjustment for voters who say they are likely to vote, 32% back yes, down from 42% in April; 68% say no – up from 58%.

Overall, Labour is on 37%, unchanged from April. The Conservatives are on 36%, up one. The Lib Dems are on 15%, unchanged, and others on a combined 11%, down two.

ICM interviewed a random sample of 1035 adults aged 18+ by telephone on 2-3 May 2011. Interviews were conducted across the country and the results have been weighted to the profile of all adults.