It was an iconic moment in British politics: on the morning of 11 May 2010, after five days of uncertainty and coalition negotiations, Gordon Brown resigned as the UK’s prime minister. He concluded his statement by thanking his wife Sarah “for her unwavering support and her love, and for her own service to our country”. Then the couple opened the famous black door of No 10 Downing Street to bring their two young sons out to join them. Hand in hand, the Brown family posed for photographs, before walking away down the road where cars waited to take them away, out of the public eye.

Since Labour’s election victory in 1997 until this departure 13 years later, Sarah Brown occupied the rarefied, ill-defined role of political spouse. First as the partner of the Chancellor of the Exchequer, and then from 2007 of the Prime Minister, she worked on the world stage – both supporting her husband and running the charity she founded in 2002, now known as Theirworld. She is also well known as an early and enthusiastic adopter of social media, joining Twitter in March 2009 and making news later that year when she overtook Stephen Fry as Britain’s “highest profile Twitter user”.

Given her facility with digital media, perhaps it isn’t that surprising that Brown is a keen podcast listener. When we spoke over the phone, she told me that she “dips in and out of an awful lot of things”. She started off with audio interviews that charities she was interested in posted on their websites, but once she had a podcast app on her phone her tastes broadened considerably. “At the beginning it was probably things like Mystery Show or Guilty Feminist, or listening to all of Serial,” she said. She also likes The Urbanist, and uses the BBC’s podcasts to keep up with radio shows she doesn’t get time to listen to live, like Desert Island Discs or Graham Norton on Radio 2.

Probably her favourite podcast, she says, is Stuart Goldsmith’s The Comedian’s Comedian, in which Goldsmith, himself a stand-up, interviews a fellow comedian about how and why they work as they do. “Even though that's not necessarily my subject area or where I have any expertise, I just find that deep conversation with someone about the way they work really interesting and it really works on a podcast format,” Brown said.

To fit her listening into her busy life, Brown – like most of us – uses podcasts to keep her company while she does other things. “I think the way I listen is mostly either walking or when doing something around the house. . . When I was in the States [on a recent extended trip], I tried using podcasts for running, and it wasn’t very successful. Music is definitely better for running, but podcasts work for long walks or chore-type things around the house.”

Recently, Brown made the transition from podcast listener to podcaster herself. At the beginning of November, she launched her own show, Better Angels. It’s an interview show that focuses on activism and campaigning, with an emphasis on practical actions that can bring about social change.

“I think we're all quite overwhelmed by the darkness of news and big events, and in 2016 that feels even bigger than ever,” she told me. “I feel there's a strong appetite for good news and good stories, and to my mind there’s a huge number of people – both well-known people and people who are quietly doing their own thing – who have extraordinary stories to tell. I'm interested in why they do it, and how they get to do it, and what the outcomes are.”

From her listening to shows like Serial and Untold: The Daniel Morgan Murder that have a strong series arc, Brown realised that she wanted the opposite for her podcast. “I wanted to make sure each episode stood on its own,” she said. “Even though you would like people to listen to each episode, I wanted to create something that could start anywhere, so you could enter it for anything that interests you.”

Initially, she thought she wanted the show to be long interviews with particular individuals. Her guests so far have included the former First Lady of South Africa and widow of Nelson Mandela Graça Machel, the comedian David Baddiel and the economist Larry Summers, and the topics covered include getting started with activism, finding inspiration and the power of laughter.

However, once she began recording the conversations, she realised that she could do more than just publish the interviews on their own. “There were quite strong themes emerging [in each interview],” she said. “You realise that each episode is going to have three, four, five, six different voices in it, and that you need to develop a kind of narrative arc for each episode.”

When I asked Brown why she felt that a podcast was the best vehicle for what she wanted to do, as opposed to doing a high-profile media interview or making a series for an established broadcaster like the BBC, she explained that the decision had its origins in her use of Twitter, and her struggle to overcome her fear of public speaking.

“If I look at my own history, I was very happy to run a business, or be involved in a charity, but I was never a public face of it,” she explained. “With a time in government, I realised that I had my own voice, and that I could do useful things if I used it.

“It’s fairly well documented that I had a pretty torrid time learning how to speak publicly. During the time in government I used Twitter. . . I understood that I had quite a public face, and you have a responsibility to share and be transparent about what you're doing, but I wasn't sure that I could navigate my way at that time through the British media.”

Twitter enabled Brown to get her statements out directly, without mediation and on her own schedule. The media could then pick them up and report them, but she was in control of the message. It was a similar realisation that made her realise the potential of podcasting as a way of communicating her ideas directly to interested listeners. “I'm not going to be able to run around and make television programmes all day long,” she says. “And I wanted to make something that can capture other people's voices.”

As Brown described her process for making Better Angels, I realised that she means just what she says about wanting to be personally involved in what she puts out. Perhaps surprisingly for a public figure of her stature, she does a lot of the work herself.

“I've started with a Tascam recorder and a couple of really nice microphones that I can take around myself and set up myself,” she explained. “Then it's very easy for me to just download the interview and stick it onto a computer, listen to it and decided what bits I want to include.”

She has editing help to put the show together, and records her introductions and narration at a studio in Edinburgh she borrows from the People’s Postcode Lottery charity. “As long as someone sets me up in the corner, it's amazingly easy,” she said.

Like many podcasters, the desire for more and better recording equipment has already hit her. “I'm getting quite nerdy about it,” she said. “I'm coveting the next microphone and the next bit of soundproofing.”

Six episodes of Better Angels are completed, and Brown is already thinking about the next six, and the six after that. Her dream guests, she told me, would be Tina Fey and Amy Poehler “because they're quite astute about social change at the same time as being really excellent comedians” and the new UN Secretary General, Antonio Guterres, who takes office on 1 January. “I don't know if I'll get him but I'll certainly try,” she said.

Perhaps the assumption will be that a podcast by the wife of a former Prime Minister will be a short-lived publicity exercise, but Better Angels is much more than that. Brown is a sympathetic and confident interviewer, and the theme of her show – that progressive social change is possible if you work hard and strategically towards it – could hardly be more relevant at the moment. She has excellent contacts from her time in Downing Street, and says that so far when she asks people to be on her podcast, “nobody says no”.

As for how long she will keep going with it, Brown told me that she has no intention of stopping any time soon. “I've got a list of a hundred ideas – whether I will get to a hundred episodes I don't know, but I might.”

Do you have ideas for podcasts I should listen to or people I should interview? Email me or talk to me on Twitter. For the next instalment of the New Statesman’s podcast column, visit newstatesman.com/podcasts next Thursday. You can read the introduction to the column here.