Support for the Conservative party has plunged since the budget according to the findings of a new Guardian/ICM poll that gives a resurgent Labour its best score in almost nine years.

The three-point lead David Cameron was enjoying over Labour immediately before George Osborne's budget has now given way to an eight-point deficit.

Tory support has plunged by six points in a single month, down from 39% to 33%. Meanwhile, Labour has climbed five from 36% to 41%, to claim an eight-point lead. The Liberal Democrats stand still on 15%, while the combined total of the smaller parties has inched up two to stand at 12%.

The results include adjustments which ICM makes for the likelihood that respondents will actually turn out to vote, and also for the historic reluctance of Tory voters to identify themselves.

These refinements have improved ICM's accuracy over recent elections, but without them the Labour lead would be even bigger – as it has been in some recent surveys by other companies.

The Conservative slide is the biggest seen in the monthly Guardian/ICM series since the autumn of 2008, when the onset of the credit crunch briefly produced very volatile political conditions.

It leaves the Tories with their worst score since before the general election. Labour, meanwhile, has exceeded the 40% threshold – often said to be the benchmark for a clear election win – for the first time in many years. Indeed, its 41% score is the party's strongest showing in the series since May 2003.

At that time, Iain Duncan Smith was heading the embattled Tory opposition to Tony Blair's government, and Labour will be thrilled at the thought that the fallout from the budget and other problems such as the petrol panic may now have landed David Cameron's party in comparable difficulties.

But the detail of the poll does not suggest a sea change in public opinion. On the crucial question of economic competence, in particular, the government remains comfortably ahead – with Cameron and Osborne trusted to run the economy properly by 44% of respondents, with 31% believing Labour leader Ed Miliband and his shadow chancellor, Ed Balls, would provide more effective financial management.

This continuing 13-point margin will be a great comfort to the Conservatives, although the trend is now running against them here too.

At the end of last year, Cameron and Osborne led Miliband and Balls by 21 points on economic management, a gap which narrowed to 18 in January and 17 just before the budget, before narrowing by another four points this month.

Ratings for individual politicians suggest that the headline Labour lead is driven more by disillusion with the coalition than by any positive view of the opposition.

By wide margins, voters reject the idea that any of the three party leader "understand people like me", and also the suggestion that any of them are "good in a crisis".

On both scores, Miliband's standing is somewhat worse than his already negative scores in December.

The big difference, however, concerns Cameron's perceived competence. At the turn of the year, by 50% to 40% voters trusted him to do well in a crisis. But that 10-point advantage has now turned into a 13 point deficit, with voters now rejecting the idea that he is good in a crisis by a 50% to 37% margin.

The poll asks about voting intentions for Westminster as opposed to the upcoming council elections, where there has been speculation that fringe parties may do well.

Some recent polls have shown a surge in support for the UK Independence Party (Ukip), suggesting it could even push the Lib Dems into fourth place. But ICM puts it on just 3%, up two points from 1% a month ago.

The UK scores for other smaller parties are: 4% for the Scottish Nationalists, 1% for Plaid Cymru, 2% for the Greens, 1% for the British National Party and 1% for other minority groupings.

ICM Research interviewed a random sample of 1,000 adults aged 18+ by telephone on 20-22 April 2012. Interviews were conducted across the UK and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.