More voters now say they would back the Brexit party at the next general election than the Conservatives, according to the latest Opinium poll for the Observer.

Nigel Farage’s party increased its support by three points to 24% of the vote, leapfrogging the Tories and trailing Labour by just five points. The Conservatives claimed 22% of the vote, the same figure they recorded in last week’s poll.

The Brexit party also maintained its 14-point lead when voters were asked who they would back in next week’s European elections, maintaining 34% of the vote. Labour secured 20%, with the Liberal Democrats up to 15% support. The Tories were on 12%, up one point on a week ago.

While the Remain vote remains split between several parties, the Lib Dems have become the top choice for Remain voters. The party increased its share of Remain voters to 29%, up seven points. Labour’s share of Remain voters was down three points on 28%.

The poll found that if Labour were to switch and clearly back a second referendum with an option to remain in the EU, the party could win back a large number of Remain votes in Thursday’s vote. In such a scenario, Labour’s vote share increased to 30%, a 10-point increase on its current position.

Support for Theresa May is ebbing away, even among Tory voters. Two in five (38%) 2017 Conservative voters think the prime minister should resign immediately. It has increased from a third (32%) since before the local elections in April.

Theresa May and Jeremy Corbyn are now tied over who would make the better prime minister, though both have low ratings. Each has only 19%, with 55% saying that neither would be the best person for the job.

Until recently Remainers dissatisfied with the major parties have struggled to unite around a single pro-Remain party Adam Drummond, Opinium

Support for May’s deal appears to have hit a ceiling. For the first time since the indicative votes in the House of Commons took place, more of the public think that MPs should vote the deal down (39%) than vote for it (36%).

Adam Drummond, head of political polling at Opinium, said: “While the home for dissatisfied Leave voters was established quite early on as Nigel Farage’s Brexit party, until recently Remainers dissatisfied with the major parties have struggled to unite around a single pro-Remain party. However, with less than a week to go there are signs that the Liberal Democrats are emerging to fill this slot. Although their share of the Remainer vote (29%) is nowhere near the 63% share the Brexit party has among Leavers, they have overtaken Labour (28%). The question is whether that trend continues in the few days of campaigning left.

“Labour’s difficulties on Brexit are further highlighted by what happens when we test some scenarios. When we ask what voters would do if the Tories were able to pass Theresa May’s deal and that MEPs elected next week would never take their seats, there is almost no change in the Conservative vote share. In contrast, when we present the scenario of Labour unambiguously committing to a second referendum with Remain being on the ballot, Labour pulls back 10 points to be level with the Brexit Party on 30%.”

• Opinium polled 2,009 people online between 14-16 May.