Support for Nigel Farage's party rises to 20% in relation to May's elections, compared with 35% for Labour and 25% for Tories

Ukip can expect the support of one in five voters in May's European elections, the latest Guardian/ICM poll shows, although Nigel Farage's party remains in third place behind Labour and the Conservatives.

The research reveals that Ed Miliband's party remains comfortably in the lead when people are asked about the European elections – on 35%, with the Tories in second, on 25%. The pro-European Liberal Democrats languish on 9%, just ahead of the Greens, who are on 7%.

These results adjust for the expected rock-bottom turnout in the ballots for Brussels – just 27% of respondents said they were certain to vote, just half the proportion for Westminster – and differ considerably from the headline results, in the regular Guardian/ICM question about general election voting intentions.

Compared with last month, Labour climbs three to 38% in the Westminster stakes, but the Tories also advance two, to 34%, so the four-point lead enjoyed by Ed Miliband's party is only one point more than in January.

Both the big parties' advances come at the expense of the Lib Dems, whose dismal European prospects come coupled with a February Westminster score of just 10% – Nick Clegg's worst ever score with ICM, and a depth the party has only once hit before during the last 20 years, in September 1997 – the height of Tony Blair's honeymoon.

This means that Ukip – who, days ahead of the Manchester Wythenshawe byelection, climb by a single point to 11% – have now pushed the Lib Dems into fourth place in the traditional state of the parties poll, for only the second time ever in the series.

If Ukip can be cheered by that, it might have hoped to be in a stronger position by now in relation to Euro elections that are now a mere three months away. If its support remained at 20%, that would represent a three-point advance on the 17% showing it achieved in 2009, which was then sufficient for second place.

But in the actual vote in June of that year, which took place in the twin shadows of the MPs' expenses crisis and the great recession, there was also strong support for various other rightwing and religious fringe parties, competition that has now disappeared.

In 2009, the neo-fascist British National party came in on 6%, and both the anti-Celtic English Democrats and a Christian political alliance achieved 2% apiece.

None of these groupings is registering significant support in the latest's poll, and their lost votes – in combination with the supporters the Conservatives have lost since 2009 – might have been expected to provide Ukip with an even bigger boost.

Ukip can, however, point out that its final tally in 2009 exceeded its strength in surveys at the time – and insist that it will exceed expectations again.

But as things stand, Conservative support in the European elections is holding up reasonably well against 2009, down by just three points against a baseline year in which, on the opposition benches, the Tories enjoyed commanding leads in most Westminster polls.

Labour, meanwhile, looks poised to rebound strongly from the record-breaking depths that Gordon Brown plumbed that year. If, as the poll suggests, Labour comes home with 35%, Miliband will have more than doubled Brown's mere 16% in 2009.

In both the European election and Westminster surveys, this month's polling also provides rare signs of solidity in support for the Labour/Conservative duopoly, whose grip is often said to be weakening.

The detailed breakdown of the general election voting intention data shows both the main parties are shoring up core elements of their support.

During this parliament, Labour have been polling particularly well among women, and this month their score among female voters rises to 43% (up from 38% last month). Conservative reliance on older voters has developed in parallel, and in Monday's survey the Tories command an outright majority support – 51% – of voters aged 65+.

But perhaps the most closely-watched sub-group of the entire electorate are 2010 Liberal Democrat supporters, the voters who may well hold the key to election 2015. This month, remarkably, more of them – 34% – are actually signalling that they will switch to Labour, than the 30% who are planning to stick with Nick Clegg.

In the European election polling, the only minor party to record an significant score that is not separately shown is the Scottish Nationalists, who are on 3%. In the Westminster polling, the SNP are also on 3%, as are the Greens.

• ICM Research interviewed a random sample of 1002 adults aged 18+ by telephone on 7-9th February 2014. 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.