The party, fronted by Farage and founded only last month, would take 34 per cent of the vote in the May 23 election, compared with 21 per cent for Labour and just 11 per cent for May's Conservatives. The Liberal Democrats would get 12 per cent.
Opinium's separate poll asking how people would vote in the event of a general election, showed May's Conservatives, on 22 per cent, trailing Labour by six percentage points and ahead of the Brexit party by just one point.
May and Labour's Corbyn are scheduled to hold more talks next week to try to find a Brexit compromise, but getting any deal through Parliament will be tough.
One of the main claims made by Farage, formerly of the right-wing UK Independence Party, is that millions of Britons would desert the two main parties for the new Brexit Party if May and Corbyn reach a consensus.
The poor polling will pile the pressure on the British Prime Minister, who has been told by an influential group of Conservative lawmakers that she should set a date for her departure next week.
Graham Brady, chairman of the 1922 Committee, which can make or break party leaders, told BBC Radio that May had been asked to give "clarity" in a meeting with the group next Wednesday, after she failed to get her Brexit deal through Parliament, leaving the government in a state of limbo.
"It would be strange for that not to result in a clear understanding [of when she will leave] at the end of the meeting," he said.
May, who secured the leadership in the chaos that followed Britain's 2016 vote to leave the European Union, has promised to step down if lawmakers back the deal she struck with Brussels to leave the bloc.
But the Prime Minister has lost heavily on three attempts to get it through Parliament, defeated by lawmakers in her own party who want a much more comprehensive break from Brussels and those who want a second referendum to reverse the process.
Brady, head of the group which oversees the party's leadership contests and represents the wishes of backbench lawmakers, said he thought May had been reluctant to set a date because of the impact it would have on any future Brexit vote.
"I think the reticence is the concern that by promising to go on a certain timetable, it might make it less likely she would secure parliamentary approval for the withdrawal agreement, rather than more likely," he said.
Tensions within the Conservative Party have grown after May failed to deliver Brexit on the original deadline of March 29. May has since opened talks with the opposition Labour Party to try to find a compromise before the next departure date in October.
Telegraph (London), Bloomberg, Reuters