'The Brexit Party' led by Nigel Farage is polling higher in Britain than the two major parties combined, ahead of European election later this month.
The party is on course to get 34% of the votes, according to the latest Opinium poll for The Observer there.
UK Labour are on 21% and Theresa May's Conservative Party are in fourth place on 11%.
The pro-EU Liberal Democrats are in third place on 12%.
The poll of 2,004 people also asked voters about their intentions in the next general election - Labour leads this with 28%.
The Conservatives are on 22%, just 1% ahead of the Brexit Party.
Despite the dominance of Brexit as an issue, many British voters do not know where each party stands on it - 36% were not aware of the Conservative stance and 38% were not aware of Labour's.
General election poll
In a separate survey by ComRes for the Sunday Telegraph, Mr Farage's party has overtaken the Conservatives for the first time in a new general election poll.
The 'Brexit Party' is one point ahead of the Conservatives in what would be their worst ever result, according to the survey.
Andrew Hawkins, the chairman of ComRes, described the poll as a "disaster", adding: "If the Conservative leadership contenders are not careful, there will be no party for them to lead."
Mr Farage launched his party in April, announcing his aim to take on the political establishment, which he accused of betraying Leave voters.
British Prime Minister Theresa May has been in talks with Labour leader Jeremy Corbyn in an effort to reach a Brexit deal that will be passed by parliament.
Mrs May has tried and failed three times to get her own deal passed by MPs.
The Opinium poll comes after both Labour and the Conservatives were punished by voters in the local council elections.
Elections for the European Parliament are to be held on May 23rd and Britain will take part, after failing to leave the bloc by the initial deadline of the end of March.
Britain is now due to leave the EU in October.