Doing better than the hapless Brian Paddick in the recent London mayoral elections isn't quite storming the Winter Palace, but let's not be too picky. On 3 May, the Greens got 4.48% of the vote to Paddick and the Lib Dems' 4.16% – which meant that while Green candidate Jenny Jones mustered around a tenth of the support given to Boris Johnson, her party definitely came third, and thereby decisively entered mainstream politics. Possibly.

Anyway, with that triumph in the bag, the Greens now want to capitalise on the Lib Dems' national woes, and work on an aspiration voiced in the Guardian by the up-and-coming Green activist Adam Ramsay. "We should be saying: 'We can replace the Lib Dems as the third party'. In terms of any given issue, we have more popular support. There are lots and lots of people in this country who are very angry, but haven't entirely lost faith in party politics and representative democracy, and that requires some leadership: people saying, 'We're going to do this – come and join us.'"

Here, though, is the interesting twist. Though the great Green breakthrough has yet to materialise, the party's slowly rising profile has been embodied by Caroline Lucas, the Greens' leader, and the MP for Brighton Pavilion (where they also run the city council). Now, though, she is going to step down – in order, she says, "to broaden opportunities for the range of talent in the party and to raise the profiles of others aspiring to election". Her replacement could be one person, or two – because, the Greens being reliably forward-thinking and iconoclastic, the post is available as a job-share.

So, what if Nick Clegg's treacherous no-marks were pushed aside? It may be a long shot, but with the Lib Dems having recently registered poll ratings of as little as 8%, it may be worth thinking about.

Over to Green deputy leader (and likely top-job contender) Adrian "no relation to Adam" Ramsay: "It would reinvigorate our democracy," he says. "The Lib Dems' betrayal of their supporters has been a tragedy because it has made people cynical about politics. But we can provide an alternative, for people who voted for them in good faith, because they wanted a fairer society, to protect public services, and defend the environment. People want to see a party with practical, radical policies."

The aforementioned Jenny Jones has ruled herself out, so is he minded to go for the leader's job? On this subject, Green radicalism slightly recedes into the distance, and he sounds a note of grim political orthodoxy: "I shall be making an announcement in due course."