Being “elevated” to the peerage is not dissimilar to turning 21. It doesn’t really change how you feel, and you’re left wondering what all the fuss was about. It’s what happens afterwards that has a far greater chance of changing you. Jenny Jones is finding this out for herself. “I don’t feel any different, personally… but people treat you differently because of the peerage thing”, explains the only member of the Green Party to sit in the House of Lords. “I’m an egalitarian, so this idea of prestige, and priority and elitism really sits quite badly with me”.

Baroness Jones 1 (John Francis)

Jones has not always rubbed shoulders with Britain’s governing elite. Born in Brighton in the late 1940s, she spent her formative years living in Moulsecoomb, a council estate in the suburbs of the town. Her family were “the last in our street to get a fridge, a phone and a TV”. After a stint as an archaeologist she took up politics, joining the Green Party in 1988. She has been a member of the London Assembly since 2000 and served as Deputy Mayor between 2003 and 2004. When we meet in the foyer of the Thomas Paine building, it is not one month since she was “ennobled” – she stretches the “o” to give the word a sarcastic gravity – in a ceremony stuffed with the pomp and pageantry of which Jones is so wary.

But she has brought her childhood in Moulsecoomb with her. She took the estate’s name for her title – “Moulsecoomb is where I got my world view” – and is determined that she will not lose the sense of normality it gave her. “I think I’m relentlessly normal”, she says. “Staying in touch with how life is lived” is very important to her; she does not want to lose sight of this when surrounded by all the “weirdnesses” of the Lords. She is troubled by the gap between the governed and the governing and worries that it has a deleterious effect on policy making. “How can you make legislation for the majority of people if you can’t hear what the majority are saying?”

How does she reconcile her new position with her belief in egalitarianism? “I’m not a revolutionary”, she says. “I’d rather work within the system and try to improve it”. I ask her how much she think that one peer in 800 can hope to achieve? “I’m not sure what one person can do”, she concedes, but she maintains that “there are probably other people in the House of Lords who’ve got green ideas – who are greens, that’s just not what they call themselves… If we work together we could make a difference”.

The Greens are used to working with other political parties. With often-limited numbers, they have to. Jones recalls her work on undercover policing: “I would constantly get shouted down by the Tories”. But eventually she got them to pay attention. “I bought a copy of my police file [citizens have the right to request copies of information that certain public bodies hold on them], and I showed the Tories. And they were furious about it! Not because of the spying but because it was a complete waste of money!” What sort of information had they collected? “It’s stuff I’d tweeted, or they’d got from newspapers, or even from our press releases”. She suspects that she may, at last, have found a receptive audience. “At some point you can engage other political parties in what is potentially not their thing, as it were… You just have to make it relevant to that person”.

Is the same true for climate change? “It’s hard for people to understand how dramatic it is”, she tells me. But she predicts that the public will become more aware of the scale of the problem once it affects them personally – for example, “when it starts to impact on our food supply”. She argues that the issue is very much intertwined with economic security: “if people can’t pay their bills, or feed their kids, then they haven’t the time to worry about environmental issues”.

On the subject of the cost of living, what does she make of Ed Miliband’s proposed energy-price freeze? “I think it’s gimmicky”, she says. “There are better things he could do”. She cites the Europe-wide energy market as a key reason why politicians would struggle to artificially lower prices. Nevertheless, “it’s great that he’s stirred up that debate”. What would the Green Party do? They would “make sure the energy companies pay their green taxes”, she says, and then use this money to reduce energy demand in the long term by investing in energy saving measures. “And you’ve got to go all out for renewables… Diversify: that’s the secret to survival”.

Jones had hoped that the price freeze would be the start of a shift to the left for Labour, although she now thinks that that seems unlikely. But where she seems disappointed by Miliband, she is contemptuous of the coalition. “This government’s a disaster”, she tells me. “It’s cruel, you know?” Much as she dislikes the word, she believes that we need a more “holistic” approach. The government wants to reduce expenditure in the short term but often overlooks the fact that making cuts now can often lead to greater costs in the future.

With so much of her work to date being based in London, she works with Boris Johnson’s administration in City Hall much more than with central government along the river at Westminster. She stood against him for the London mayoralty in 2012. “I do find Boris an incredibly difficult personality”, she says. But he does have his advantages: “I’ve met Arnold Schwarzenegger! It’s one of the few things I’ve got to thank Boris for”.

Our conversation instantly turns from politics to celebrity. Jones is an Arnie super fan! “He speaks seven languages; he’s an incredibly bright guy… And he came from a very poor background in Austria – you’ve got to admire him for what he’s done”. The man himself was in London shortly before the 2012 mayoral election. Jones chanced upon him and Boris waiting to get into a lift, and “I squeezed through the crowd with my elbows”. I cannot help but imagine her clawing through in the manner of a One Direction fan girl. And what did he say? “Hello, Jenny Jones”. She does a very convincing accent. This spontaneous insight into her taste in popular culture, right at the end of our talk, neatly underlines her cherished normality. Try to imagine what Cameron or Miliband would have done in that situation.

The House of Lords is centuries old, and it is hard to deny that it increasingly looks its age. Change comes slowly to such places. But if Jones can hold on to her professed normality – she seems to have done so thus far – and whether or not you agree with her politics, Baroness Jones of Moulsecoomb may yet do Parliament a great deal of good.