Ukip is on course to win the highest share of the vote in next month's European elections, senior political figures warned on Sunday, in a result that would be viewed as a collapse of trust in the political establishment.

With a European election poll showing Ukip forging ahead, after a week that saw the party involved in a row about a racist candidate and buffeted by other controversies that would damage conventional parties, Peter Hain, the Labour former cabinet minister, said Ukip seemed to be immune from criticism and that he expected the party to beat Labour.

Lord Tebbit, the former Tory chairman, also said he expected Ukip to make history by becoming the first party other than Labour or the Conservatives to win a UK-wide election since the first world war. Tebbit said his party was still paying the price for David Cameron's decision to brand Ukip supporters "fruitcakes, loonies and closet racists" eight years ago.

At the weekend, Ukip became embroiled in a fresh racism row following revelations that William Henwood, a local election candidate for the party in Enfield, north London, had said Lenny Henry should emigrate to a "black country" after the comedian and actor suggested ethnic minorities were poorly represented on British television.

Asked to explain himself on Sunday, Henwood chose to repeat the racist sentiment. He told the BBC: "I think if black people come to this country and don't like mixing with white people why are they here? If he [Henry] wants a lot of blacks around, go and live in a black country."

But a European election poll for the Sunday Times giving Ukip a three-point lead suggests scandals are not causing harm. The poll was conducted at the end of last week, after a controversy over a racist local government candidate, Andre Lampitt, and questions raised by the Times over party leader Nigel Farage's office expenses. The YouGov survey put Ukip support at 31%, ahead of Labour on 28%, the Conservatives on 19% and the Lib Dems on 9%. Of 16 European election polls conducted this year, this is only the second showing Ukip ahead, and the first showing a lead higher than two points.

Hain said the mainstream political parties had to recognise that Ukip's success was symptomatic of a wider loss of trust in politics. "The political class needs to wake up because Ukip are capitalising on the big anti-politics sentiment that is out there," he told the Guardian.

"Despite the fact that their candidates have blamed flooding on gay marriage, called women sluts, and expressed openly racist and Islamophobic prejudice – some really nasty stuff – and Nigel Farage has been accused of all sorts of allegations, all of it just seems to wash off, just like water off a duck's back, because they are the expression of a deep antagonism to the political class.

"It is really disturbing that they seem to have developed an immunity to the truth. It's for that reason that I expect them to be in the lead on 22 May."

Hain said Labour could win, but that it would be "very hard" and that the party would have to get its vote out effectively. His analysis was backed by Matthew Goodwin, an associate professor of politics at Nottingham University and co-author of a new book about Ukip, Revolt on the Right. He said that, until recently, he had expected Ukip to come second in the European elections, but that he had changed his mind.

"Having looked at the shift in opinion polls in the last 10 days to two weeks, I think what we are beginning to see is what we saw at this point before the 2009 European elections and the 2004 European elections, which was a Ukip surge, which always happens late on," he said. "My instinct is that they will probably end up ahead at the European election."

Goodwin said there were two reasons why the extensive media coverage over recent days of scandals and embarrassments involving Ukip did not seem to be having any impact on the polls.

"First, the core Ukip electorate are the most distrustful in British politics," he said. "And, second, over the last 20 years in European politics, one of the lessons that has been learned has been that, when it comes to the radical right, the strategy of condemnation and of ridicule has got us nowhere."

Goodwin added that a Ukip victory in May would have profound implications. "If they finish second, that raises awkward questions for David Cameron. But if they finish in first place, that amounts to an entire rejection of the British establishment's political class."

Tebbit said the party was a "quite remarkable phenomenon" and that it seemed to be "inured" to attacks from the media. "On present form, it looks like they will poll the most votes," he said, claiming the Ukip supporters who commented on his Telegraph blog constantly referred to Cameron's decision to label them "fruitcakes, loonies and closet racist" (a claim Cameron has subsequently retracted) as one reason for their rejecting the Conservatives.

Cameron's jibe was a terrible mistake, the peer said. "If I were running a retail business, and if I suddenly discovered that my customers had been walking past my shop and going to a competitor, I would not stand in the street cursing them. I would go to the other shop and see what they were selling," he said.

Jeremy Hunt, the health secretary, said that the comments from Ukip's Henwood about Henry were "absolutely disgusting".

While promising to investigate Henwood's comments, Ukip declined to disown him outright, instead claiming that the party was the victim of smear campaigns orchestrated by other parties alarmed at Ukip's success in the polls.

• This article was amended on 28 April 2014 to correct a quote from Matthew Goodwin.