Overgrown gardens spill over the sandstone walls and onto the quiet, sloping streets. A grinning graffiti skull and a church spire mingle in an unconventional skyline. Shops sell handmade pottery and vegan supplies. Academics pass artists and scientists on the street. If there is such a thing as the typical Green constituency, it probably looks a bit like Bristol West.

In 2015, a Labour candidate, Thangam Debbonaire, took the seat from the Liberal Democrats, with 22,900 votes, and a majority 5,673. But in second place, with 17,227 votes were the Greens. And this general election the candidate is the most high profile yet – the MEP and economist Molly Scott Cato.

I meet Scott Cato on a bank holiday Monday in the new Green party office, where volunteers are piling placards and arranging signs. Maps of the constituency are pinned to a wall. “What has changed is last time was that lots of people really wanted a Green MP but they didn’t believe they could make it happen,” Scott Cato says. The 2015 election made it seem possible. She argues voters are rebelling against the first past the post system: “People aren’t prepared to settle for the Tweedledee and Tweedledum of politics.”

The Greens are often pilloried as almond milk-guzzling climate warriors. But Scott Cato wears jackets – colourful ones - and talks about clamping down on tax havens more than the transition movement. As an MEP, she can also talk with authority about Brexit.

Molly Scott Cato with Green Party activists in Bristol West

Roughly three quarters of voters in the area voted to stay in the EU (in Bristol as a whole the vote was 62 per cent Remain). The incumbent Labour MP Debbonaire is also anti-Brexit. She defied the party whip and joined the one existing Green MP Caroline Lucas in voting against Article 50. But while Labour struggles on a national level to define its position on Brexit, the Greens are calling for a “ratification referendum” on the final UK-EU deal. “Somebody came into the shop yesterday, and said ‘Would you vote against triggering Article 50?’” Scott Cato recalls. “That was easy – it was definitely yes.”

As this suggests, Scott Cato does not spend her time on the doorstep simply debating climate change. In addition to Brexit, voters are worried about the lack of affordable homes. On Twitter, Scott Cato shares messages in support of refugees, against privatisation of the NHS and local businesses. She visits the mosque to hear about Islamic banking and discuss the British government selling arms to Saudi Arabia.

Scott Cato says it is “a bit of a myth” that Green voters are middle class: “If you look at their voters their incomes are below average. That’s not surprising – we campaign for progressive taxation.”

All the same, when I meet Alex Teague, a Green party member, who has just been out handing flyers, he believes the demographics of Bristol West are part of the story.

A chemistry teacher, he did a PhD in environmental science, and argues that this middle-class, university area is the “ideal constituency” for the Greens: “It is left leaning, liberal.” He tells me the city has one of the highest concentrations of PhDs and medical graduates in the country (when I look into it, I find that according to the 2011 census, Bristol ranks 63 out of 359 in the most qualified areas of England and Wales).

Teague describes himself as a “socialist and environmentalist” and wants a party that can “look 50 years into the future”. When I ask him about Brexit, he jokingly asks me: “Can I just have a little cry first?”

Still, for all the Green posters unfurling in the bay windows, the party’s victory is far from certain. As I wander to St Werburghs, a neighbourhood known for its city farm, a wildlife centre and a sustainable self-build housing programme, I pass terraced brick houses with Labour posters in the windows.

When I speak to Debbonaire on the phone, she argues that there is nothing the Greens can do that she isn’t doing already. “The Greens have been talking a lot about a progressive alliance,” she says. “We already have one – it’s called the Labour party.” As for the environment, Labour’s commitment to tackling climate changes “is in its constitution”. A resident of the constituency for 26 years, she says the response on the doorsteps has been positive: “People are happy with how I have been as an MP.” They are aware that she voted against triggering Article 50.

Debbonaire was one of the MPs who publicly criticised Jeremy Corbyn in the summer of 2016, when she described how he had appointed and then sacked her from a role in the middle of her cancer treatment. Bristol has an active branch of Momentum, Corbyn’s grassroots organisation. So can the party overcome its internal divisions?

“I think when you come to a general election, Labour members want to elect a Labour government,” she says. Her message to Bristol’s Corbynites is: “If you want to have a Labour Prime Minister, you want to have Labour MPs.”

So far, this seems to be resonating. Ollie Turnbull is a member of the People’s Assembly Against Austerity, a forum for anti-austerity views founded in 2013 by figures including the late Tony Benn, Jeremy Corbyn and the Green MP Caroline Lucas.

In his work as an activist, he hears less about Brexit per se, and more concerns about “a Tory Brexit”. He is wary of the Green demand for a second referendum, and thinks a Labour-led deal could turn the situation “into a positive”.

Indeed, for all Labour’s dismal national poll ratings, Corbyn seems to have invigorated the party's supporters I encounter in Bristol West. In 2015, the Greens were the only party to put “end austerity” on their manifesto. Other policies now echoed by Labour included raising the minimum wage to £10 an hour and scrapping tuition fees.

For Turnbull, it’s enough to sway him. “I voted Green in 2015,” he says. “I won’t do so this time round because the Labour party is offering a genuine alternative.” The Greens may have long been the revolutionary party in Bristol West. But since 2015, Labour has experienced a revolution of its own.