Taxi drivers can normally rely on doing excellent business at party conferences, ferrying VIPs, delegates and lobbyists to and from the secure zone of the venue. But the drivers outside Birmingham's New Street station on Friday enjoyed no such boom. "The Green party conference? Haven't heard of it," said Malik Gasam, one of the drivers in the scarcely moving rank. "I haven't taken any fares for that."

Instead, on the other side of the station, greener transport awaited: a small group of volunteers directing a steady stream of walkers bearing green badges and many in sloganned T-shirts to the venue for what promised to be one of the party's biggest conferences. More than 750 delegates were expected, most, but not all, members of their local organisation and at least 40% first time attendees, many of them new members who have swelled the party's ranks to a record 18,000 even as other political parties are losing members.

The Greens are in feisty mood, buoyed by a good showing in the recent European elections, when they received more than 1.2m votes. Leaders are seeking to reposition the party as a leftwing alternative to Labour, with far more than just their stalwart environmental policies: a higher minimum wage than Labour is advocating; a halt to the "creeping privatisation" of the NHS; and the scrapping of tuition fees, including retrospectively on fees already paid.

"We are the real opposition," Caroline Lucas, the party's only MP, will tell delegates on Saturday. She will barely mention the governing coalition, focusing instead on a fight against Labour.

Anthony Pearce of the Stafford and Stone branch agrees. "I was a lifelong Labour supporter, over 30 years. But it became very difficult to see any difference between their policies and the Conservatives. Eventually I left and came to the Greens."

Terry White made a similar journey from the Liberal Democrats. "It was tuition fees," says White, 21. "The Lib Dems were not in tune with young people." The Greens are currently polling at 6.6%, which is neck-and-neck with the Lib Dems.

In hoping to challenge the UK's three-party hegemony at next year's general election, the Greens are strikingly similar to another small party on the other end of the political spectrum. But while Nigel Farage, the UK Independence Party leader, is a familiar fixture on TV and front pages, the Greens have struggled to gain recognition.

One of the key problems is the party's struggle – like Ukip's – to break beyond the perception of it as single-issue. "We are called the Green party, and we have a lot of environmental policies," says Ankaret Harmer, a member in Birmingham. "But actually it is a lot broader than that, though some people don't realise. We have policies on everything."

"There isn't enough awareness [among voters at large] of the range of policies we have, our social justice policies," says Rosie Pearce, aged 19, who studied all of the UK's political parties before deciding that Green policies most matched her outlook. "We need to raise awareness of that." Pointedly, Lucas will spend only a few minutes on green issues – fracking, nuclear power and weapons – with the rest on the social justice policies.

Money comes into it, too. Whereas the major party conferences are a boon for big business, with multinationals and lobbying groups, the Green party stalls include the Stop the War Coalition, Dignity in Dying, Friends of the Earth, the Quakers and a handful of others. Several trade unions are present, including the RMT, NUT and TUC.

For years, the Greens also suffered from internal disorganisation. "We were not nearly as organised as we should have been," says one delegate, who did not wish to be named. "I've been told it was quite chaotic before. It's not like that now," says another new member.

But the complaint that comes up most frequently from delegates is that the media ignores the Greens while lavishing attention on Ukip. "If you look at the political parties that get the most coverage, they speak for business and the establishment. Media organisations are businesses and they follow that," says Terry White.

Vicky Duckworth adds: "There should be more coverage of us, we have done as well [electorally] as Ukip."

"It's because Ukip are the establishment, not challenging the establishment," says Rosie Pearce. "We are scaring them." Penny Kemp, from London, says: "It's not even just about Ukip – they [the media] should be giving us as much attention as they do the Lib Dems – we are polling the same as the Lib Dems, so why aren't we getting recognition for that?"

Ukip's policies and the Greens' could scarcely be more different. The Greens are pro-Europe and sympathetic to immigration, attacking policies they say hurt people on benefits such as the bedroom tax, strongly in favour of renewable energy. (One of Farage's favourite topics, after immigration and the economy, is wind farms. He doesn't like them.) In style, too, they are poles apart. The party's democratic structure would never permit the kind of brutal tactics employed by Farage, when he ousted Roger Lord as candidate for Clacton, in favour of the Tory defector, Douglas Carswell. (The disgruntled Lord warned in the Guardian: "Can anyone really trust him? Would you really sign a treaty with this man?")

Demographically, Ukip's core support lies among older voters while the Greens appeal strongly to the young. "Young people have suffered a real kicking from austerity," says Pearce. "Our policies are very popular with the young," adds Vicky Duckworth.

Sahaya James, aged 16, who joined nearly a year ago, agrees: "We have very strong policies on issues that affect young people, like tuition fees, but also the NHS and creating high-quality jobs. I think young people do respond to what we have to say – we want a sustainable future."

That may bode well in the longer term, but young people are less likely to vote in next year's general election. Women are also well-represented, with the party leader, MP and peer all women, and policies advocating gender equality.

For the Greens, the last few years have been encouraging, with the first Green MP and peer, rising polls and new members. But the challenges the party will face in the general election are stark. Media interest or lack of it, tight budgets, the perception of the party as a fringe interest, all will play a role.

For the delegates in Birmingham, the best hope lies in distinctive leftwing policies. "When I speak to people, they understand our policies, they like them," says Anthony Pearce. "It's about getting people to think, and being bold – not just accepting the status quo, but rethinking it," adds Anne Critchley, 72, who joined two weeks ago. "I don't believe Ukip want people to think."