When Siobhan Benita joined the Liberal Democrats in 2016 after the EU referendum result, campaigning for the party felt very different. “I’m from Kingston [in south-west London] and we knew we had support there, but outside that you still had to work very hard to get people to have a conversation with you. A lot of people were saying ‘we’re not forgiving you for the coalition’,” she said. “But now a lot of that has been overtaken by Brexit.”

Out campaigning in west London on Sunday for the European parliament elections, Benita – now the party’s London mayoral candidate – said familiar complaints about the Lib Dem coalition with the Conservatives and the raising of tuition fees had barely been mentioned on the doorstep in recent weeks.

The group of activists had been buoyed by polling from Opinium published in that day’s Observer which put the party in third place with 12% of the vote, ahead of the Tories on 11%. The survey had Nigel Farage’s Brexit party in first place with 34% and Labour second with 21%. The Lib Dems made big gains in this month’s local elections, winning 10 councils to add to the seven they held already, and 704 councillors.

In the last EU elections, in 2014, the Lib Dems lost 10 MEPs, leaving just one – Catherine Bearder in the south-east. This time they hope their unequivocally pro-EU stance – with the slogan “Bollocks to Brexit” and support for a second referendum – will win them support in remain-voting heartlands, particularly in London and the south-east.

Against that optimism is the contention that even a good result for the party is likely to pale into insignificance against the wider consequences of the vote. On Monday Labour’s deputy leader, Tom Watson, said there were “only two forces that can win” in the EU elections: “that nasty nationalism” of the Brexit party, or the “tolerant, compassionate outward-looking patriotism” of Labour.

Labour has urged remain supporters to support it as the only force that can stop the election being understood as a resounding endorsement of Farage and his allies.

Bearder disagrees. “To stop Brexit you need to vote for a remain party,” she said. “And is Labour remain? Nobody quite knows if Labour is remain. The Liberal Democrats is the party that is committed to stopping the chaos that is Brexit. Labour will continue it, Farage will continue it and the Conservatives will continue it.”

Knocking on doors on a leafy street in the Labour-held parliamentary constituency of Ealing Central and Acton, Irina von Wiese, a Lib Dem MEP candidate, said she had spoken to many lifelong Labour voters who were planning to vote Lib Dem next Thursday. Sixty per cent of voters in Ealing voted to remain in the EU.

“In my local party of Hammersmith and Fulham we’ve had about 20 new members since the local elections, of which at least three came over from Labour, and that’s because of Brexit,” she said.

The Lib Dem leader, Vince Cable, who has said he will step down this summer, said the party’s EU election campaign did not aim to change people’s minds about Brexit but to persuade decided remainers to lend their vote.

“We are not trying to win over Brexiteers,” he said. “There may become a point at which we get a referendum and that battle for the hearts and minds will take place, but this isn’t it. We are basically trying to get remain voters to get behind us.”

Cable said he was optimistic his party would win more MEPs in the south-east, London and the south-west. He said the Lib Dems were now hopeful they could secure some MEPs in the north, something they didn’t initially think would be possible. “We’re not going to get lots of MEPs,” he said. “But we hope to have a respectable showing. We only won one last time, so it’s difficult to go backwards.”

A woman accosted by cheery Lib Dems as she pushed her grandchild in a pram said she had never voted Lib Dem before but thought she would do so this time in protest against Brexit. “Normally I’d vote for Labour, just because of where I’m from and my background, being working class,” said the woman, who did not want to be named. “Everyone else [other than the Lib Dems] is a bit wishy washy. I really don’t want us to leave and I was so gutted after the referendum.”

Asked about anger at the Lib Dems in coalition, she said: “The whole landscape has changed now and so I guess the way people vote is going to have to change as well. I don’t know if people have really forgiven them. I think I have,­ but I can’t speak for everyone.”

Cable has said he regrets that the Lib Dems were not able to fight a “common campaign” with Change UK, the new party formed of breakaway Labour and Tory MPs. But he said the rival party did not seem to be making much headway.

“To the extent to which we can divine what’s going on, they are not providing much competition,” he said. “They’re showing a bit more in London than elsewhere, but there is very little support that we’re registering at the moment.”

Although Cable denies that his party’s success in the local elections was down to Brexit opposition alone – he points to gains in areas such as Barnsley and Sunderland – he admits Brexit has boosted its support. “We do have pretty solid policy and philosophical thinking and values,” he said. “But it has needed something to trigger people’s imagination and build up a real strength of conviction behind campaigning. And I think Europe has done that for us.”