“You only have to cast your eyes along those green benches to think this place doesn't really represent modern Britain,” said Caroline Lucas, the UK’s only Green MP, of the House of Commons. “There are lots of things you could do about it, and one is say: ‘Why not have job share MPs?’”

Politics is full of partnerships and rivalries, but not job shares. When Lucas and Jonathan Bartley were elected co-leaders of the Green party in September, they made history.

“I don't think any week's been typical so far,” said Bartley, when I met the co-leaders in Westminster’s Portcullis House. During the debate on the Hinkley power plant, he said, Lucas was in her constituency: “I was in Westminster, so I could pop over to do the interviews.”

Other times, it’s Bartley who travels: “I’ve been over to Calais already, and I was up in Morecambe and Lancaster. It means we’re not left without a leader.”

The two Green leaders have had varied careers. Lucas has become a familiar face in Parliament since 2010, whereas Bartley has spent most of his career in political backrooms and wonkish circles (he co-founded the think tank Ekklesia). In the six weeks since being elected, though, they seem to have mastered the knack of backing each other up. After Lucas, who represents Brighton Pavilion, made her point about the green benches, Bartley chimed in. “My son is a wheelchair user. He is now 14," he said. "I just spent a month with him, because he had to have a major operation and he was in the recovery period. The job share allows that opportunity.”

It’s hard enough for Labour’s shadow cabinet to stay on message. So how will the Greens do it? “We basically said that although we've got two leaders, we've got one set of policies,” said Lucas. She smiled. “Whereas Labour kind of has the opposite.”

The ranks of the Greens, like Labour, have swelled since the referendum. Many are the usual suspects - Remainers still distressed about Brexit. But Lucas and Bartley believe they can tap into some of the discontent driving the Ukip vote in northern England.

“In Morecambe, I was chatting to someone who was deciding whether to vote Ukip or Green,” said Bartley. “He was really distrustful of the big political parties, and he wanted to send a clear message.”

Bartley points to an Ashcroft poll showing roughly half of Leave voters believed capitalism was a force for ill (a larger proportion nevertheless was deeply suspicious of the green movement). Nevertheless, the idea of voters moving from a party defined by border control to one that is against open borders “for now” seems counterintuitive.

“This issue in the local election wasn’t about migration,” Bartley said. “This voter was talking about power and control, and he recognised the Greens could give him that.

“He was remarking it was the first time anyone had knocked on his door.”

According to a 2015 study by the LSE researcher James Dennison, Greens and Kippers stand out almost equally for their mistrust in politicians, and their dissatisfaction with British democracy.

Lucas believes Ukip voters want to give “the system” a “bloody big kick” and “people who vote Green are sometimes doing that too”.

She said: “We’re standing up against the system in a very different way from Ukip, but to that extent there is a commonality.”

The Greens say what they believe, she added: “We’re not going to limit our ambitions to the social liberal.”

A more reliable source of support may be the young. A May 2015 YouGov poll found 7 per cent of voters aged 18 to 29 intended to vote Green, compared to just 2 per cent of those aged 60+.

Bartley is cautious about inflaming a generational divide, but Lucas acknowledges that young people feel “massively let down”.

She said: “They are certainly let down by our housing market, they are let down by universities.

“The Greens are still against tuition fees - we want a small tax for the biggest businesses to fund education because for us education is a public good, not a private commodity.”

Of course, it’s all very well telling young people what they want to hear, but in the meantime the Tory government is moving towards a hard Brexit and scrapping maintenance grants. Lucas and Bartley are some of the biggest cheerleaders for a progressive alliance, and Lucas co-authored a book with rising Labour star Lisa Nandy on the subject. On the book tour, she was “amazed” by how many people turned up “on wet Friday evenings” to hear about “how we choose a less tribal politics”.

Nevertheless, the idea is still controversial, not least among many in Nandy's own party. The recent leadership contest saw a spate of members ejected for publicly supporting the Greens, among other parties.

“It was like a witch hunt,” said Lucas. “Some of those tweets were from a year or two ago. They might have retweeted something that happened to be from me saying ‘come join us in opposing fracking’, which is now a Labour policy. To kick someone out for that is deeply shocking.”

By contrast, the Greens have recently launched a friends scheme for supporters, including those who are already a member of another party. “The idea that one party is going to know it all is nonsense,” said Bartley. “That isn’t reality.”

Lucas and Bartley believe the biggest potential for a progressive alliance is at constituency level, where local people feel empowered, not disenfranchised, by brokering deals. They recall the 1997 election, when voters rallied around the independent candidate Martin Bell to trounce the supposedly safe Tory MP Neil Hamilton. Citing a recent letter co-signed by the Greens, the Scottish National Party and Plaid Cymru condemning Tory rhetoric on immigrants, Bartley points out that smaller parties are already finding ways to magnify their voice. The fact the party backed down on listing foreign workers was, he argued, “a significant win”.

As for true electoral reform, in 2011, a referendum on changing Britain's rigid first past the post system failed miserably. But the dismal polls for the Labour party, could, Lucas thinks, open up a fresh debate.

“More and more people in the Labour party recognise now that no matter who their leader is, their chance of getting an outright majority at the next election is actually vanishingly small,” she said. “It’s in their interests to support electoral reform. That's the game changer.”