The Green Party believes it is within 2,837 votes of electing its second-ever MP in Britain

But there is drama playing out in marginal constituencies, and none is more unusual than Bristol West. This section of the city is a straight fight between Labour and the Green Party. The Tories and the Liberal Democrats are very unlikely to win here. Going by the election result from 2015, Green Party candidate Molly Scott Cato only needs to peel 2,837 votes from Labour to win.

That makes Bristol West the constituency that the Green Party most believes will give it its second-ever MP, after Brighton’s Caroline Lucas.

The drama is heightened by the fact that Bristol West’s voters are incredibly fluid in their voting allegiances. In 2010, Lib Dem candidate Stephen Williams won the constituency and the Greens polled less than 4%.

But in 2015, Labour won, and the Greens ran a decent second place. The results looked like this:

Labour
Green
Lib Dem
Conservative

Only half of that 5,673 gap between Labour and the Greens needs to switch, which is why Bristol West is the Green Party's No.1 priority this year.

Until last month, the Greens were actually favourites to take the seat, according to bookmakers. That changed after the local elections on May 5, in which the Green candidate did poorly, coming fourth in Bristol overall and third specifically in the Bristol West boundary.

Now bookmaker Paddy Power has the Greens at 15/8 odds to win, and Labour’s Thangam Debbonaire at 8/11.

"I would say 30 to 40% [of voters] are still mulling over their choice," Scott Cato told Business Insider. "A quarter of people will vote by post."

Bristol — like Brighton — is not like other British towns. It is a hive of liberalism, pro-European in its outlook, and full of avowedly leftist students. The Green Party has 1,400 members here. About 50 of them are working on Scott Cato’s campaign.

"Behind every door there is a highly educated person wanting to talk about politics. … I've never seen anything like it. It's an amazing electorate here, really well-informed, and they’re polite and charming too," she says.

Unsurprisingly, Bristol is also a strong Remain area. Seventy-nine percent of people voted to Remain in the EU Referendum last year. With the Labour Party officially supporting Brexit, and the Lib Dems unable to win, that makes Scott Cato the only place to go for angry Remain voters. The Green Party’s official policy is to hold a second "ratification referendum" to give people a choice between either approving the Article 50 deal or remaining in the EU.

Scott Cato is the sitting member of the European Parliament for the South West of England, and is positioning herself as the only candidate in the race who actually knows what she is talking about when it comes to the EU.

"The Labour candidate has accepted that Brexit is a done deal and they are not offering a referendum on the terms of the deal, they are just saying there should be a parliamentary vote, that’s Labour’s position. Since this parliament will be dominated by Conservatives, a parliamentary vote will be lost. So they’ve effectively surrendered over Brexit," she says.

She is also part of a new generation of Green politicians who are determined to take politics — and actually winning power — seriously. The class includes Brighton's Caroline Lucas, the Isle of White's Vix Lowthion, and London Camden councillor Sian Berry — all women, and all often more eager to talk about housing, the NHS, and economics than they are about climate change or pollution. The Greens have stopped campaigning in neighbouring Bristol North West in order to give the Labour candidate a better shot at winning there — that's how serious they are about yanking the few levers of power within their grasp.

To win in Bristol, a lot of things have to go right for the Greens. The Lib Dem vote has to fail, even though its candidate came second to Labour in the mayoral election in Bristol West. The national trend of pro-Brexit Labour voters drifting off to the Conservatives, mistrustful of Labour leader Jeremy Corbyn, has to continue. And Debbonaire’s local popularity has to wane.

That’s a big ask.

So what about that weakness at the local elections? "Our focus was aways the parliamentary seat. Also, it’s a very small turnout, about 35%, so I really don’t think you can draw strong conclusions," Scott Cato says.

When asked if she really thinks she has the best chance of winning, she says: "Numbers matter in elections. Because of the percentages last time, I’d have to say I do."