At the end of the summer, Swedish singer-songwriter Jenny Wilson returned with 'Autobiography', the first bit of new music from her forthcoming album, Demand The Impossible. Predominantly instrumental, 'Autobiography' is a slow build-up of a vocoder-dance thunderstorm and the perfect calling card for a project heavy with personal experience as well as growth. Beginning with a broody piano and increasing in might with every bar, a blustery, impossible-to-ignore rhythm section then takes over proceedings with a simple four-liner soliloquy, making succinct and poignant reference to Wilson's recurring battle with breast cancer. "Cannot put it down with words\cannot put it down with letters\the scar is my only proof\the scar is my autobiography," she sings and draws the listener in with an effortless swoop.

An alumnus of First Floor Power, a late-90s Swedish pop outfit whose live shows inspired The Knife's 'You Take My Breath Away' (to which Wilson contributed vocals), the 38 year-old released her debut solo record, Love & Youth back in 2005 and, despite sounding like a slightly poppier, Scandinavian version of Joni Mitchell, she has somehow escaped the glare of the commercial spotlight outside her homeland. So much so that her 2009 masterpiece, Hardships!, and its 2011 re-recorded counterpart, Blazing, didn't even get a UK release. "I would love to have released all my albums here and for them to have been successful here," Wilson sighs, "but, you know, I have had some bad luck with that and also I got sick at the wrong time. I have been so frustrated about that because I feel that my albums should have been known to more people. I guess they are well-kept secrets," she says, reconciled.

The good news is that the reason The 405 manages to get face-to-face time with Wilson in London is that she's in town to make plans for a live show here early next year. And this time round, UK fans won't have to resort to imports in order to hear the new album, with Sony Sweden and Gold Medal Recordings bringing it out here as well.

Wilson began work on Demand The Impossible last year, after finishing her Scandinavian tour of Blazing. Shortly after the creative process for the album commenced, however, she found out that her cancer had returned. "I had to pause things for some time and then go on with it all later," she says. Despite difficult medical treatments, losing her hair and a considerable time spent in hospitals, Wilson kept focusing on getting back to business and, whenever she could, continued doing work on the record even during what she refers to as her 'toxic treatment' phase.

I ask her whether she feels that the shape of the album changed between the first stage of recordings and the subsequent resumption. "Yeah, I think so," she nods. "I kind of knew what I was trying to say before, but then afterwards I definitely knew. It cemented it. It was, like - OK, now I totally know what I want to say. I had this dreamy vision, like the idea that I wanted to write about my body and also society and pieces of various other things but then they blended together. I also found I had more energy, whereas before I didn't. So I was like 'fuck everything!' I was kind of pissed off - but in a good way, I think. In an empowering way."

There are two songs on the album, 'Restless Wind' and 'Autobiography', where Wilson talks about her scars. "I think in my art, in my lyrics, it's easy to talk about almost anything because that is the way like to do it," she says. "I like to do it very personal. I don't want it to stay private, I want to invite other people in so that they can understand what it is to have a scar, even if you don't have a scar yourself. So I try to talk about it in a metaphorical way. The 'Autobiography' lyrics might be the best lyrics I have ever written. They're so simple."

Is that why you chose that song as the album's introductory track, I ask. "Not because of the lyrics, actually, but because of the epic, cinematic soundscape. We thought it would be very fun to do something visual with it because it's not a single, it's not a poppy tune and it is certainly something very different from everything that I had done before. You can hear it from the first note - this is not the old Jenny Wilson." I argue that, at the same time, 'Autobiography' does have hints of her quintessential sound. As does the album. "I think that's perfect, then," she says. "It's not that I don't want to be that Jenny Wilson that came up with Love & Youth, Hardhsips! and Blazing but I have been travelling far this time to get somewhere else with the sound."

The tracks where Wilson's sound gives proof of her travelling farthest are 'Opposition' and 'My History', both of which bring in a Middle-Eastern vibe. "I had a lot of Arabic sounding tunes in my head," Wilson recalls, "and I had been listening to a few Arabic tracks which had this very attractive energy and beauty so I did it my way and put it all into the soup." On 'Opposition' she sings: "You're gonna give me my freedom back?\I'm trading the salt of my tears\I'll give you the dark pearls of my blood". It is the album's opening track but it was actually the last song recorded for it. Wilson explains: "Almost all the tracks I do... I work on them for a long time and struggle with them a lot but with that one I just recorded and made the whole thing very fast. I was alone in the studio and it was there in my head, complete. I instantly loved it and I was hoping that my drummer and engineer would like it too when they returned to the studio. I played it to them and they were, like - 'shit, it's really rhythmic, how did you do that?' - and then we replaced the programmed drums with live drums and took it from there."

Weaving through the album is an alter-ego narrator through whom Wilson elucidates some of her views on the world. "You could say that this character comes in and out, throughout the whole album more or less," Wilson says. "I had this idea of... if you imagine this kind of street prophet, standing in the middle of the road - you know, that very annoying person who is also a very wise dude, pointing at things and picking on people and merging thoughts into something new. And that was a way that I wanted to write lyrics this time. Like a beat poet. Taking inspiration from things that are happening right now and also from inside of yourself. Mix those philosophies. I was not afraid to use old legends or God or Judas [on 'Battle With God'] or anything. I'm just mixing everything and it's the crazy touch on that which I like. Have you seen the record cover, yet? That's me as that character who is doing the talking."

Wilson talks about putting things into the mix, putting them in 'the soup'. And on the track 'The Soup' we are transported into a soup kitchen, where Wilson explores her feelings about the human condition. It is also the very first track she penned for this record. "I wrote it many years ago," she says, "and it sounded pretty much the same, although I've changed a lot along the way, of course. I didn't have the full lyrics at first, I only had the line "Oh, do you want to taste soup?\come on take a sip from the spoon." That was it. And I thought, that's so stupid, that's so annoying. What a very childish rhyme! But then in the process of making Demand The Impossible I got into this idea of the street prophet dude and the lyrics then came to me right away. I suddenly understood what it was about. For me that song is a lot about how things are in the world right now. It's getting crazier and crazier and people are getting more and more lost. So much poverty. Even in Stockholm - there are beggars everywhere. You can't walk anywhere without seeing it."

On 'University of my Soul', our street-prophet gets his own preacher's monologue, giving voice to Wilson's frustrations: "Libraries are shutting down\Schools are burning down\Our leaders must fall down and let the women wear the crown\Let them take over\From the underground\To the streets, to the churches\From the cities to the deserts\To the parliaments." More interlude than an actual song, 'University of my Soul' nevertheless maintains the album's momentum and, sitting at the halfway mark of the record, acts as a focal point for its ideas.

On a record with practically nothing worth skipping, it's difficult to pick a favourite, but a definite highlight on Demand The Impossible is the fifth track, 'Mean Bone', on which Wilson's voice tackles the verses with a completely new timbre for the singer. When I mention this, Wilson smiles and nods. "Yeah, would you like to know the secret? I was really, really ill. I had fever and my throat was sore and I got back to the studio and couldn't even talk. And someone said to me - 'you should probably try singing, then, because your voice would sound really cool.' And I was like - OK [simulates croaky voice]. I tried to sing, I went for it and when I sang those lines the song didn't really exist, yet, but I took those lines and put them together and it just worked."

Wilson and I turn to chat about her songwriting method. "With 'Opposition' I had a melody in my head that I was humming for a couple of weeks. In that sense that song was one of a kind. But for other songs I would say that I mostly work like this: I come up with some kind of idea of how to create a universe and I collect a lot of pictures and poems and stuff that I think has something to do with it. And I write a lot of lyrics that I collect," she says. Does she keep it all in a notebook? "Yeah, I have a lot of notebooks and I google pictures and have files on my computer with moodboards and inspirations. When I am making the arrangement, I always start with the drums. I programme the drums and I try to explore different sounds for the drums but mostly it takes a long time for me to find the right feeling for each song. I never start with a guitar or a piano anymore. I used to before but not on this record."

I ask her how 'Autobiography' started its way, seeing as the rhythm section doesn't actually come in until the 1:45 mark. Was it the lyrics we mentioned earlier? "That one actually ended with the lyrics," she tells me. "But it started because I actually wrote that track for another thing, an art installation and it was originally called 'Evolution' and had no vocals on it. I was thinking about it as an evolutionary thing - starts very minimalistic and then grows. I really, really loved that track and I took it to my drummer and we started to jam on it. I felt frustrated because I didn't find it interesting enough as an instrumental. I felt like I needed something more to happen and then that little song, the four lines of lyrics happened."

The art installation in question was 'Kate Millett Farm' by Sisters of Jam and the four songs Wilson wrote for the project (which included the original version of 'Autobiography') reflected Wilson's take on the feminist ideas expressed by Millett, the renowned American writer and activist. "I think music is the most instant way of making an audience feel something," Wilson says. "But if you put it together with pictures or a performance of some sort or build a story around it, it grows and can take you even further and that is very interesting to me. I once did a performance at an art gallery called 'The Blow', for which I wrote a 15-minute piece of music - we choreographed a boxer to the music and she was boxing through this soundtrack in a smoky room - it was very intense, powerful and fantastic. I think I try to be more flexible nowadays and braver and I think it is great to do things I haven't done before and collaborate with people that I maybe shouldn't collaborate with.

Before returning to London (as well as Paris and Berlin) in the new year for some live dates, Wilson is currently in rehearsals for her first Demand The Impossible shows in Sweden and Denmark. I ask her which of the new songs she is most looking forward to performing live. "I think it's 'Pyramids (Rose Out Of Our Pain)', actually," she says. This 5-minute tribal, rhythmic number will also be the next single from the record, following Wilson's current pop-stormer, 'The Future', which premiered last month. "Pyramids is one of my favourite tracks. It's a song about the suffering of old times and this is a song where I am really taking stuff from wherever and smashing it all into one piece. The lyrics are so well written [she laughs at the boast]. I really love the line "pyramids rose out of our pain" because, to me, that in itself says so much. Pyramids are such a strong symbol. Such great imagery. I think I got a lot of personal aggression into that one. It's a furious song."

Wilson has already filmed the video for the single (due for release in January) with long-term collaborator, Daniel Wirtberg, who also directed the videos for 'Autobiography' and 'The Future'. "I love doing the videos," she says. "I wish I had some time to play around and experiment with more videos." I ask her whether there are any visual plans for other tracks from the record. "I'm going to do one more or maybe two more," she confirms. "I think they will be for 'Ghost Station' and maybe for 'University of my Soul' as well."

Our time's up and we say our adjö. On my way home from the interview I re-listen to the new album and I'm reminded of a statement Wilson makes on her press release for it: "what else can one do when you're a citizen in a society that's fucked up? Go out and demand the impossible!" - not a bad motto, that!

Jenny Wilson's Demand The Impossible is out now on Sony Sweden/Gold Medal Recordings.