An ecstatic Nigel Farage hailed the Ukip's strong showing in the Eastleigh byelection as a sign of "revulsion" at the three main parties across Britain.

Sounding hoarse following a night of celebrations, after Ukip beat the Conservatives to second place, Farage ruled out any deal with the Tories as long as the "con man" David Cameron remains leader.

The Ukip leader took to the airwaves after his party scored its best result in a Westminster byelection, when its vote soared by 27.8 percentage points to secure second place.

The Liberal Democrats, who first captured Eastleigh in a 1994 byelection, held the seat, although its candidate Mike Thornton saw the party's vote fall by 14.48 percentage points. The Tory vote fell by a similar amount (13.96 points) as it came third. Labour trailed in fourth place, though its vote increased marginally by 0.22 points.

A relieved Nick Clegg tweeted: "Congratulations @Mike4Eastleigh: welcome to the team! We're on track for 2015 now."

The remarks by Farage came as modernising Conservatives warned the prime minister against responding to Ukip's success by moving to the right. Gavin Barwell, the Conservative MP for Croydon Central, tweeted that it would be wrong to focus solely on immigration, welfare and Europe at the general election.

In a sign of sensitivities, Barwell appeared to have removed the tweet and then tweeted: "Re previous retweet nothing wrong with any of these policies but why no mention of quality of NHS care, cost of living, help for pensioners?"

Michael Gove, the education secretary, dismissed the support for Ukip as signs of a protest vote. "People recognise that it's tough but there was no dissent from the proposition that David Cameron is taking the right decisions on the economy," he told BBC Breakfast programme.

But Farage warned that Ukip now poses a major threat to all the parties. He told Radio 4's Today programme: "The Ukip messages are resonating with people and we are daring to talk about things – like open door immigration – that everybody else simply wants to brush under the carpet and not discuss. There is [also] an increasing revulsion at three political parties who frankly look the same, sound the same and don't offer any real policy differences."

The Ukip leader was dismissive of the Tories as he mocked them as a minor party. "If the Conservatives hadn't split our vote we would have won," he said, adopting the language the Tories normally use about his party.

Farage rejected the idea of an electoral pact with the Tories as long Cameron remained leader as he made clear that Ukip was picking up votes across the board. "That is false arithmetic," the former City trader told Today of the idea that Ukip is only picking up disaffected Tory voters. "Only a third of the Ukip vote in this byelection came from the Conservatives. Two thirds came from people who either weren't going to vote at all, or from Labour or from the Liberal Democrats.

"Whilst our effect on the Conservatives is psychological – and that is huge and that is undeniable – the arithmetic does not say the Conservatives failed because of Ukip. The Conservatives failed here because traditional Tory voters look at Cameron and ask themselves: is he a Conservative? And they conclude, no, he is not. He is talking about gay marriage, wind turbines, unlimited immigration from India, he wants Turkey to join the EU."

Asked whether he would form an informal pact with the Tories, Farage said: "I do think it is unlikely we can do a deal with the Conservative party all the while Mr Cameron is in charge. Frankly I view him as a con man. I don't believe anything he says. He has made promises before on referendums on Europe and he hasn't fulfilled him. And into the bargain he is repeatedly abusive and rude about our party and the people that vote for him."

Farage, who faced accusations of being "frit" after he declined to stand in the byelection, denied that he regretted his decision. But there was a slight hesitation in his voice as he said: "We had a very good candidate and Diane James had my 100% support. I don't think I would have got any more votes than she did. I really don't."

The Tories' third place will put pressure on Cameron. Ministers had warned in private that third place would create a crisis for the prime minister, though there is unlikely to be any serious challenge to his leadership. Critics will say his gamble of pledging to deliver a referendum on Britain's membership of the EU appears, if anything, to have increased support for the only main party committed to withdrawing from the EU.