For a party pledging to renationalise the railways, a calamitously disrupted Virgin train journey to the latest campaign stop of the Green party leader, Natalie Bennett, is a gift. Stranded at Crewe, she stops short of promising trains would run on time under state control but says: "At least you won't be paying huge profits into shareholders' pockets."

The Green party, hoping to triple its number of MEPs to six and add 10% to its 140 local councillors in Thursday's elections, is direct about its radical pitch to voters.

"We need to entirely reshape our society so it works for the common good, not just the interests of the 1%, and we need to do this using just one planet," says Bennett.

The biggest crowd-pleasers at public meetings are, she says, rail nationalisation, removing the profit motive from the NHS and ending student tuition fees. "At some point we have to say austerity has gone too far. Things like social care have to be paid for."

Pollsters and political pundits judge the Greens' target for added seats to be plausible if ambitious. But they note that their poll rating of around 8%, while ahead of the Lib Dems in some polls, is similar to that at previous European and local elections. "However, because the Lib Dems are doing so badly, the Greens could finish fourth," says Anthony Wells, at polling company YouGov. "That will be seen to be a big success for them, even if it isn't really."

Like all parties in the late stages of a campaign, they are focussed on ensuring their supporters vote, and the first stop is an anti-fracking camp in a field at Upton, near Chester. Amid the tents, dogs and a piano on a pallet, a friendly reception greets Bennett and college lecturer Peter Cranie, the Greens' lead MEP candidate for the north-west of England. He lost to the BNP's Nick Griffin by 0.3% in the last European elections and the morning after also lost his job. "It was the worst 24 hours of my life," he says.

Anti-fracking campaigner Susan Burt has switched from voting Tory to the Greens. "What the main parties are doing on fracking is evil – it's the biggest threat to our country since the second world war," she says. Cranie says the issue is a clear vote winner for the Greens. "We will see peaks around the north-west, where people are worried about fracking."

Nearby in Liverpool, Green party activists prepare for canvassing with lunch at the Green Leaves veggie and vegan cafe on Lark Lane. Tom Crone, the Green council candidate for St Michael's ward by Sefton Park, says he is anticipating a complete Lib Dem collapse in the city. Lib Dems ran the council until 2010 with 46 of 90 seats, but could be left with just a handful after Thursday. "Liverpool was one of the biggest hit by council spending cuts," Crone says. "We could become the official opposition," he adds, though the council will remain overwhelmingly Labour.

Green party candidate Tom Crone canvassing in the St Michael's ward in Liverpool. Photograph: Christopher Thomond for The Guardian

The Greens have targeted the ward for several years and the initial doorstep support is enthusiastic. "We vote for them because of what they believe in, mainly the environment and they are very good on the local area," says resident Barbara Thew. "Little parties can make a difference and if enough people vote for them they can become big parties."

But there are also knock-backs. One lady complains about an unresolved bin problem, while another says: "I don't really know much about you." The firmest rebuff comes from a retired man, who declines to give a reason just as firmly.

"Immigration always comes up at some point," says Crone. While Green window posters are most common, Ukip banners can also be seen. Nationally, the pro-Europe Greens back a referendum on EU membership. "We trust the voters," says Bennett. She argues concerns about immigration stem from failed employment, housing and health policies, not the arrival of migrants.

YouGov's Wells praises the Green's ability to concentrate their vote. "The greens have been very good at targeting support," he says. "In the last local elections Ukip came second in the vote but didn't get that many councillors: the greens are the complete opposite, throwing everything at certain places and doing well." As with previous local and European elections, the Green's vote share leaps from the tiny 1% or less support they typically get in general elections.

However, across the European Union, the party looks set to lose MEPs: polling predicts a drop from 48 MEPs to 38. Claude Turmes, a long-serving Green MEP Luxembourg, blames the austerity after the 2008 financial crash: "There have been less front pages about planetary emergencies and more on unemployment, which strengthens the parties with electorates that compete with the Greens – the far left and Social Democrats."

But Neil Carter, professor of politics at York University, asks why the anti-austerity Greens are not actually doing better in the UK. "Given the unpopularity of the mainstream parties, why is it business-as-usual for the Greens?" he says. "Ukip is doing well, so why are the Greens not making gains on the opposite side of the political spectrum?"

Carter agrees with Turmes that lower environmental concern than in the run up to the 2009 elections is a problem. "Given that people in the UK tend to see the Greens as a single issue party, that means they find it harder to attract support."

But he cites the low media profile of the Greens and their policies as the key factor. "Apart from the environment issue, people are pretty much ignorant about Green party policies," says Carter. "Nigel Farage is a high profile leader who, apart for a few recent stumbles, been playing a very effective role: how many people could name the Green party leader?"