Today, Jenny Jones becomes Baroness Jones of Moulsecoomb and she's not particularly happy about it.

"There's a clerk who reads something out. I sign and that's it. It is an absolute nothing of a ceremony that obviously means a lot," she says.

"I can't quite believe it, and I'm not sure I'll be able to believe it when it's all happened. I'm not someone who enjoys any sort of ceremony."

This nothing of a ceremony has some historic implications. While there have been peers who crossed the aisle to the Green party before, this is the first time someone has entered the Lords as a Green party representative. It's a difficult thing for the party to accept, given its radical roots and the fact it believes in a wholly-elected Lords. You even get the sense the party is embarrassed by it. Their press releases on the event don't even mention the word 'Lords' – they just refer to the 'second chamber'.

The tension can be seen in Jones' reaction too. Even her chosen name, Baroness Jones of Moulsecoomb – a reference to the council estate she grew up in – suggests a pride in her background and trace of resistance to her new job title.

"I feel completely strange about the whole thing. I never thought it would happen," Jones explains.

"I have a strong sense of tradition. I mean, I used to be archaeologist. I like continuity and stability. But I don't like inconsequential nonsense. I think we should question things.

"Some things that are traditional have to be questioned and challenged. I'll go in there with respect but perhaps not exercise as much patience as I ought to."

Most people have been supportive of Jones as she takes on the Lords role, but there have been traces of opposition from within the party.

"Green party policy, of course, is for an all-elected second Chamber," she says. "The idea of having people who political parties like without a democratic mandate is wrong. But one of the things about my appointment was that I was selected by the Green party to enter the Lords according to one-member-one-vote."

"But because we back a second chamber, we do find it sticks in the craw, as it were. There are even a few Greens who think we shouldn't have taken a seat at all. I have sympathy with that, but Greens don't believe in lots of the electoral system as it exists but we engage with it. That's what we're formed for - to engage with a system we'd like to see change in."

None of which has prevented the inevitable teasing from family and friends once the announcement was made.

"They've been taking the mickey," Jones says, smiling.

"People started curtseying when they come up to me. There's been a lot of teasing. I've been very uncomfortable with it. But then if I enjoyed it they probably wouldn't do it."

Jones is keeping her job in City Hall, where she works on the London Assembly, and the teasing has been prevalent there too. "Everyone here in the building is doing it," she admits. "Boris too. He doesn't call me Jenny anymore. He calls me baroness. He knows it annoys me."

Jones will be keeping the City Hall job while she sits in the House of Lords, which is an unpaid position, although it does include a daily allowance. "I can't even pay my mortgage if I'm not doing my job here [at City Hall]. The House of Lords allowance is £300 a day but you only get it if you go in and are seen by the clerks.

"There are no resources. I don't get staff, I don't get an office. I'm waiting on a desk, but I don't think it's likely. There's a peg for my coat.

"I'm going to use the City Hall machine to keep me current on issues. I can't use the resources for my Lords work but I can use the information over there. We're not allowed to campaign as assembly members, but over there I can campaign to my heart's content."

Campaigning is at the heart of what she wants to do, as the Green peer uses her position in the second chamber to launch coordinated political manoeuvres with Caroline Lucas, the party's sole MP in the House of Commons. The party now has the tiniest of footholds in the parliamentary machine. How does she intend to make use of it?

"I think I'm going to be driven largely at first by what Caroline is doing because it means I can crib her notes," she says. "If she's doing the energy bill or human rights then I can speak on those using her research. The only extra bit I'll be doing is on policing.

"I'm putting together a bunch of people to sit down at the end of this month and thrash through what my priorities should be - mostly Green party people, but certainly people who don't think the same way. Some different brains.

"Everyone I've talked to from all parties said it took them about a year to settle in, to understand the processes, make sure they're getting things right. So there's no point charging in and making a mess of it. You need a bit of pace, but not to be a bull in a china shop."

Jenny Jones will be 'introduced' into the Lords by Baroness Grey-Thompson and Baroness Kennedy of The Shaws this afternoon at around 14:30GMT.