Nick Clegg has surged into contention as a potential prime minister, according to a Guardian/ICM poll carried out following last night's TV leaders' debate.

A quarter of voters who watched the three leaders on the ITV programme say they will switch their vote, with most changing to the Liberal Democrats.

Clegg emerges from the telephone poll as the overwhelming winner, with 51% who watched saying he came out on top. David Cameron and Gordon Brown trail in far behind: 20% say Cameron won and 19% Brown.

The poll, based on a sample of 505 voters who had previously told ICM how they would vote, found Conservative and Labour supporters also thought Clegg won the event. While 44% of Tories thought Cameron won, 46% thought Clegg did. Among Labour voters, 43% said Brown won, and 44% Clegg.

The Guardian poll coincides with a survey of voting intentions carried out by ComRes for ITV. It showed support for the Conservatives was unchanged at 35%, with Labour down one point on 28%, and the Lib Dems up three on 24%.

Among those voters who had watched the debate, the surge in Lib Dem support was more dramatic: up 14 points to 35%, only a shade behind the Conservatives on 36%, who were down three. Labour languished in third place, at 24%, also down three.

Clegg was in high spirits today as he addressed activists at Warrington Wolves's rugby stadium to seize on the momentum generated by his TV performance. "We are now the party of fairness in British politics," he said.

"Last night's debate was an important moment in this campaign because it gave us the opportunity to say to people directly sitting in their living rooms, sitting at home, that the real choice is between the old parties and the new, different, fair politics offered by the Liberal Democrats."

According to the ICM poll for the Guardian, Clegg appears to have won the affections of voters across the board. He now runs Brown neck and neck as the man voters think would make the best prime minister, 29% to 29%. Cameron remains just ahead on 33%.

Clegg is also far ahead as the leader who offers substance over spin. Cameron comes off worst among people who saw the debate, with 47% saying he is more spin than substance against 36% who say that of Brown and 11% Clegg.

Cameron performed particularly badly with Lib Dem supporters, with 61% saying he offered spin over substance. That suggests the Tory leader's appeal to centre ground voters is faltering.

The debate had a clear impact on people's voting intentions, although the effect may fade as polling day approaches. Among people who saw the debate, 23% say they will change their mind, including 25% of Conservatives and 21% of Labour voters.

Most of them are going to the Lib Dems, with 54% of people changing their minds saying they will move to the party. A further 17% say they will switch to Labour. The Conservatives have attracted the least new support with only 13% saying they plan to move their vote to the party.

The Liberal Democrats were today hailing the leader's performance as a potential "game-changer" as a battery of early polls gave Clegg the thumbs up.

A Times Populus poll conducted last night indicated that 61% of voters believed Clegg had won the night, compared with 22% for Cameron and 17% for Brown.

Research by YouGov for the Tory-supporting Sun in the immediate aftermath of the programme put Clegg on an impressive 51%, Cameron on 29% and Brown on 19%.

A text message poll for Sky News by Fizzback also rated Clegg highest, with 37% of the 1,608 voters polled. Brown came second with 32% of the votes and Cameron lagged behind with 31%.

Cameron, who had expressed fears ahead of the debate that it might be "sluggish and slow", told a phone-in on BBC Radio Manchester: "I think he [Clegg] had a good debate but I must say I just enjoyed being able to talk to people at home, to address the questions that I think are the big questions, things like immigration, the economy and crime. I thought it was a great opportunity."

The shadow schools secretary, Michael Gove, warned that the Tories now intended to subject the Lib Dems' policy programme to intense scrutiny. He highlighted Lib Dem plans to join the euro, scrap the Trident nuclear deterrent and offer an amnesty to illegal immigrants, which, he said, lay well outside the political mainstream.

"The greater degree of scrutiny these policies have, the more that people will realise that, while Nick Clegg is a very attractive individual in many ways, the policies of his party are outside the mainstream and a little bit eccentric – not necessarily what you would want at a time of crisis and difficulty," he told Sky News.

The 90-minute leaders' debate, broadcast on ITV, was the most watched show last night, attracting an average audience of 9.4m.

Despite the polling, senior Tories said Cameron's performance showed he was "ready to be prime minister" after scoring "clear wins" on key issues.

Today, the Tory leader sought to seize back the initiative on the campaign trail with an X Factor-style project which he said would help him achieve his aim of building a "big society".

Flanked by the Take That star Gary Barlow, Cameron announced that a Tory government would introduce a national music talent competition called School Stars, which would involve local and regional heats, and would culminate in a national final in June 2011. Winners would get the chance to record a song with Barlow.

Also on the campaign trail, the Labour camp sought to talk up their leader's performance and were keen to point out that last night was the first act of a three-act drama, in a nod to the other TV debates scheduled over the next two weeks.

The home secretary, Alan Johnson, told Sky News that Brown was not a "song-and-dance man" and conceded that Clegg and Cameron were "more adept" in front of a camera. "I thought Gordon did very well. This was kind of politics unplugged; they all had to do an acoustic session and I thought that worked very well."

He added: "The event was good for politics, it was good in particular for the election and I think Gordon did very, very well ... I think Gordon took the prize on substance, Clegg on style. He outstyled Cameron but it was good for politics in general."

• ICM Research interviewed a random sample of 505 people by telephone on 15th April 2010. It reinterviewed people who had previously been selected at random who told them they would be watching the debate and had agreed to be interviewed again. The sample has been weighted to the profile of all people selected at random who previously stated they would be watching the debate. ICM is a member of the British Polling Council and abides by its rules