Support for Britain's established parties is splintering, as Ukip appears poised to break the political mould by doubling its support within a single month, according to a Guardian/ICM poll.

Nigel Farage's party has surged from its previous record best with ICM, the 9% it notched up in April, to 18% after its council election victories earlier this month.

Labour, the Conservatives and the Liberal Democrats have been left reeling, with all shedding four points on the month to 34%, 28% and 11% respectively.

For all three established parties to be falling substantially at the same time is unprecedented in the 29-year history of the Guardian/ICM series.

Guardian ICM poll May 2013

Ukip's 18% is the best it has achieved with any pollster in any of the surveys logged at UK Polling Report. It is all the more remarkable for ICM, whose careful adjustments for voters who decline to reveal their political preference smooths out the wilder fluctuations of the electoral cycle.

The Tories are plumbing depths they have not experienced in more than a decade – barring a single month in 2002, they have not fallen below 28% since Tony Blair's political honeymoon in 1997-98. The Liberal Democrats, which typically fare better with ICM than other pollsters, have not fallen below today's 11% in the series since September of 1997, the immediate aftermath of Blair's first victory.

Labour's score of 34% is a miserable platform on which to build an election victory in 2015, and is its lowest since the immediate aftermath of Gordon Brown's ejection from power in July 2010.

After weeks of publicity for Ukip's leader, a "Farage factor" is clearly evident in the personal leadership ratings. Last month voters were split down the middle on his performance – 28% saying he was doing a good job; 29% a bad job – giving a net negative score of –1.

Today, the balance of opinion is running 40%-23% in his favour, a net positive of +17. Meanwhile, David Cameron hits a new personal low of –15, and Ed Miliband picks up only one from the even more dismal record of -23 which he set last month, to stand at –22.

Lack of enthusiasm for the official opposition is matched by deep disillusionment with the government. Asked to put aside party differences and consider the decision of Cameron and Nick Clegg to govern in coalition, 49% of voters say they disapprove, compared with the 36% who approve.

In May 2010, weeks after the coalition formed, ICM asked the same question and found an overwhelming 59%-32% split in favour of a unity government.

The "none of the above" disillusionment is also evident in a surge in support for other minor parties, especially the neo-fascist BNP. It stands on 4%, up three on the month, while the Greens are on 2% and the combined Welsh and Scottish nationalists stand at 3%.

Add in Ukip, and the assorted parties formerly lumped together as "others" have a combined 27%, only one point less than the Conservatives and seven less than Labour. The score is also up on last month's combined "others" total of 16%, the highest these assorted parties had scored with ICM.

ICM Research interviewed a random sample of 1,001 adults aged 18 and over by telephone on 10-12 May 2013. Interviews were conducted across the country 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.