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Nigel Farage and Mark Reckless weren’t the only ones celebrating at the Rochester and Strood by-election last week. Ukip may have triumphed but the Green Party candidate, Clive Gregory, managed to beat the Liberal Democrats to fourth place.

The Greens achieved the same feat in October’s Clacton by-election, and in May’s European elections. And they beat the Lib-Dems to third place in 2012 in both the London mayoral and assembly elections.

Now the Greens are ahead of the Lib-Dems in some national polls, at around seven per cent. Has their moment arrived at last?

The Green surge is in large part thanks to the collapse in the Lib-Dem vote since 2010. But it isn’t only Nick Clegg’s party who are worried.

“The old, lazy analysis that the Lib-Dem vote will come to us is bollocks,” says one Labour shadow minister. “It’s going straight to the Greens or Ukip. It’s a real challenge for us.” He thinks the Greens have got better at campaigning in the Lib-Dem style of “pavement politics”, concentrating on local issues: “They’re much smarter in the way they target — there’s definitely a new maturity.”

What is giving Greens new hope is the apparent break-up of the old Westminster parties’ hold on power.

“We’ve been practising tactical voting for decades and it’s given us the failed politics we have now,” says Green Party leader Natalie Bennett. “Now people are voting for what they really believe in. We’ve reached a point where neoliberal [economic] ideas have been discredited in their own terms.”

Bennett, a 48-year-old Australian-born journalist, has been party leader since September 2012, when she took over from the better-known Caroline Lucas, the Greens’ only MP. Party membership has soared 90 per cent since the start of the year to 26,200.

Now there are calls for the party to be included in any televised leaders’ debates for the next election — though that remains unlikely.

Bennett remains upbeat. “Things are wide open, with four-way marginals,” she says. “If politics keeps changing the way it has done since the European elections, who knows?”

A recent Yougov poll found that if people thought their preferred party had a chance of winning, the Greens would come third, at 26 per cent, ahead of both Ukip and the Lib-Dems.

In truth, Bennett’s own London candidacy in Holborn and St Pancras illustrates the huge challenges the first-past-the-post system presents. In 2010, Bennett came fourth behind the Tories, with 1,480 votes — just 2.7 per cent. She emphasises that the Lib-Dem vote — they came second with 27.9 per cent, after a big campaign — is now up for grabs, while Labour may suffer as veteran MP Frank Dobson stands down. Still, she has a mountain to climb.

The Greens will stand in three-quarters of all seats, seriously targeting 12, including Norwich South and Bristol West. But polls suggest that they will be lucky to improve on their single seat, Brighton Pavilion, and Labour is fighting hard to retake that. Caroline Lucas took the seat in 2010 after the Greens poured in volunteers; the Greens also control the local council.

Nevertheless, Labour is taking seriously the threat of losing Left-wing middle-class votes to the Greens. Last summer shadow justice secretary Sadiq Khan MP was put in charge of a unit dedicated to combating the threat. Its main thrust is to emphasise the party’s Left-wing credentials to supporters alienated by Tony Blair and Iraq. Labour’s own research suggests that a majority of Greens voted Labour in 1997 and 2001; recent YouGov analysis shows that 22 per cent of Green voters were Labour in 2010 (and 50 per cent Lib-Dem.)

“Our job is to prove that we’ve changed from New Labour and that under Ed we’ve rediscovered our radicalism and are totally focused on tackling inequality,” says Khan. This week he has been talking up not just Labour’s position on climate change but the mansion tax, and its votes against intervention in Syria and for recognition of Palestine.

More negatively, campaigners are pushing the message that by denying Labour victory, a vote for the Greens is a vote for the Tories.

As Peter Kellner, president of pollster YouGov, has pointed out, the Greens are thus almost a mirror image of Ukip. Not only are their voters younger, university-educated ABC1s while Ukip voters are older, less educated and more working class, they are also forcing both main parties to woo their respective ends of the political spectrum.

“It makes it that bit harder,” says Kellner of the Green effect. “It only needs the Greens to siphon off 1,000 votes in each marginal and it could cost Labour six or eight seats.”

Take the Labour target seat of Bermondsey and Old Southwark. Labour is mounting a heavy campaign to unseat senior Lib-Dem MP Simon Hughes. September’s Ashcroft poll in the constituency put them just one per cent behind the Lib-Dems, but the Greens are on five per cent, up from 1.6 per cent last time. Even a small leakage of Labour votes Leftwards could cost the party the seat.

Labour insiders warn too of a longer-term threat, especially at London local elections in 2018: after three years of a Miliband government, Bennett’s party could capitalise on the urban Left’s dissatisfaction.

Jim Dickson, a senior Lambeth Labour councillor, has experience of such local street-fighting in Herne Hill, south London. His Labour team faced a serious challenge in May’s council elections: in his Herne Hill ward, the Greens took 28 per cent of the vote, coming second there and in two neighbouring wards. (Nationally, they hold 162 council seats.) “The Greens never quite give it the campaigning zeal they need and they have a big problem with delivery where they are elected,” says Dickson. “But where the demographics are right for them and they put the effort in, they can do well.”

His neighbourhood is classic Green territory. Many Green voters are what Experian’s Mosaic demographic breakdown of the UK classifies as “urban intellectuals”: highly educated, relatively affluent, younger, many of them public-sector professionals. There is a self-reinforcing aspect: “People like to do what they think other people like them are doing,” says Kellner.

“You’d be surprised how low down environmental issues come in these voters’ top 10 list of concerns,” says one Labour insider. Many are drawn to the Greens because of broader Left-wing economic issues such as inequality and low pay.

Bennett readily admits that commitments to renationalise the railways and abolish student tuition fees have won Left support. She seems uncomfortable with the suggestion that the party is more Left-wing now: “The Green Party has always seen the economy and the environment as indivisible.” But she concedes that “we haven’t always been as good at getting that message across, and now we’re better at that”. Indeed: her unveiling at this year’s party conference of a pledge to raise the minimum wage to £10 an hour was tactically astute.

For now, the Greens remain a party concentrated in the recycling urban middle classes. But these are strange times indeed in British politics. It is “not completely inconceivable”, says Kellner, that next May they could come fourth in the popular vote, behind Ukip but ahead of the Lib-Dems — yet get no seats. Then again, if the Greens win even a handful of their target constituencies, a Labour-led government might yet have to make peace with Britain’s most radical party.

Twitter: @hernehillandy