Ukip support has surged after its strong showing in two byelections last week, causing particular problems for the Conservatives’ ratings, according to a Guardian/ICM poll.

Ukip has bounced up five points on last month, with 14% of those polled now saying they would vote for the party. Labour remains at 35% and much of the advance made by Nigel Farage’s party appears to come at the expense of the Conservative party, which drops back two points to 31%.

The telephone poll was conducted after Douglas Carswell’s victory for Ukip in the Clacton byelection last week.

At the end of a conference season widely judged to have been a success for David Cameron, whose tax-cutting speech was well received the week after Ed Miliband was criticised for forgetting to mention the deficit in his speech, this is as low a rating as the Tories have had all year in the Guardian/ICM series.

While the poll also contains some difficult messages for Miliband on how voters rate the Labour leader personally, the Tory decline leaves him sitting on a four-point lead.

The Liberal Democrats clamber back up a single point on the month, to stand at 11%. The Greens are on 4%, the Scottish National party on 3% and Plaid Cymru on 1%.

While Farage will be delighted to bump up five points in a single month, the survey does not exactly suggest he is breaking the mould. Ukip support has been higher before – standing at 16% in June, in the aftermath of its triumph in the European elections, and it hit 18% with ICM last year after a strong showing in the 2013 council elections.

The poll asked voters “which single issue” would “concern you most when it comes to casting your vote”. The results confirm that immigration – the single issue marking Ukip out from the Tories and Labour – is identified by 20% of voters as their priority on this measure. Miliband, however, who is particularly keen to push health up the agenda, will be pleased to learn that more voters, 24%, name the NHS as their top concern, which makes it the top issue overall.

Another recent ICM survey, reported in the Guardian last week, suggested that the Conservatives have built a commanding 20-point lead on economic trust, but in Monday’s poll Labour can find some solace in the dimension of the economic agenda about which voters say they are most concerned. The top priority for 17% is “jobs, prices and wages” – an area where, as a result of stuck wages and the opposition’s “cost of living” campaign, Labour is regarded as being competitive – whereas “the government deficit” – an issue accepted as favouring the Conservatives – is the chief concern of only 7% of voters.

Other issues such as schools (the priority for 9%), pensions (5%), crime and disorder (3%) and the other great Ukip preoccupation, Europe (7%), lag some way behind immigration, living standards and health, confirming that these are shaping up to be the three key policy fields of next year’s electoral battleground.

After Ukip triumphed in Clacton and came within 617 votes of a shock win at Heywood and Middleton, voices in both the big parties have been raised to identify immigration as the principal problem that voters want to see addressed. The shadow home secretary, Yvette Cooper, has vowed to talk about immigration more. On the Conservative side, Boris Johnson embraced Ukip proposals for quota-controlled migration from Europe, suggesting that if Cameron were unable to secure this as part of his renegotiations of the terms of British membership, then the Conservatives should be prepared to campaign for Britain to quit the EU in the planned 2017 referendum.

On Monday, Downing Street was forced to clarify that the prime minister’s remarks about reforming free movement referred to more modest aims, such as extending transitional arrangements for new members states and imposing further restrictions on European nationals claiming benefits.

The poll asked voters how they rated Cameron, Miliband and Farage on specific characteristics, relating to ethos, empathy and an instinct for siding with the majority. All three ratings for all three men are negative on balance, confirming that virtually all politicians – including the self-styled outsider Farage – are mistrusted by the majority.

Miliband will be concerned that his ratings have sunk on the questions where he used to outperform the prime minister, such as whether or not voters feel that he “understands people like me”. Only 25% of voters now credit Labour’s leader with that, whereas 60% disagree, giving him a net score – the gap between these two figures – of -35. That is a decline from the more respectable -16 achieved on this question last November, and scarcely better than the net -36 rating of an Etonian prime minister who has always been vulnerable on this measure. Farage does better than both his rivals, although not spectacularly so, with a net score of -17.

Farage also does better than the mainstream political leaders on the question of honesty. Asked whether they agree that he is “more honest than most politicians”, 30% of voters agree, while 50% dissent, giving him a net -20, which compares with -31 for the prime minister and -36 for Miliband. Again, Miliband has suffered some slippage since last November, when he stood at -23.

But on looking after “the interests of the many and not the few” Miliband fares less badly than his rivals. While he cannot match the +1 he achieved on this count in April 2012, with 38% agreeing he will serve the majority and 48% disagreeing, his net negative is a comparably modest -10. That compares with -20 for both Cameron and Farage, and, given Ukip’s bold claims about its prospects in the Labour heartlands, the party will be disappointed not to have done better. Farage does fare better among the often electorally important “C2” skilled manual occupational grade, who give him a net +2 on this measure of fairness, but in the north he remains saddled with a net -25.

ICM Research interviewed a random sample of 1001 adults aged 18+ by telephone on 10-12 October 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.