The word has been used to describe Vashti Bunyan so often over the years you wouldn't be surprised to find her picture if you looked the word up in a dictionary. It's been used about her voice - a delicate, slight yet utterly beautiful thing - and it's been used about the woman, or at least the girl she was. The girl who was once signed up by Rolling Stones manager Andrew Loog Oldham. The girl who in 1970 released an album, Just Another Diamond Day, that nobody bought, a failure that crushed her will to make music for decades and saw her disappear in a horse and cart to the wilds of Scotland and Ireland. A fresh peach who was bruised by life.

But really, is that the case? Look at it from a different angle and you see a woman who committed herself to an alternative lifestyle and stayed on that path for a long time, longer than many of the other refugees from the 1960s. A woman who put aside music for all sorts of reasons - mostly negative - but who stuck to her decision. And a woman who in the 21st century has returned to her first love and has finally been able to do what she always wanted: make a record exactly the way she wanted to make it. You can use the word fragile about Vashti Bunyan, but there's a core strength in there too.

"My father used to have this word 'cussed' which he would call my mother all the time. It means just awkwardly stubborn," Bunyan remembers when I suggest as much. And yes, she admits there is something of that in her too. "I see it in my kids as well. Watching my daughter, I see a lot of me in her. She can seem like this very fragile person but actually she has a steely interior and she will not do anything she doesn't want to do. And I think that's probably how I've become. I know what I want and if I'm asked to do something I don't want to do, now I don't do it."

Lets begin with the now, shall we? Vashti Bunyan is in her late 60s, the mother of three grown-up children (and three stepchildren) and still a beauty. We are sitting outside at the Terrace Cafe in Edinburgh's Botanic Gardens not so very far from where she lives. A winter flower, she talks quietly but confidently although she doesn't really look up from under her fringe until we've been talking for an hour.

We're here because of her new album, Heartleap, seven years in the making. It is her third and possibly her last. Will there even be albums seven years from now, she asks. Heartleap comes almost 10 years after Lookaftering, her second, and 44 years after her debut Just Another Diamond Day, which has become a cult album over the years and an emblem of a hippy alternative lifestyle.

But Heartleap is, at last, the record she has always wanted to make. Not because she has a problem with Just Another Diamond Day (although there was a time …) or Lookaftering. But because she has been in control of this album and she's gone her own sweet way on it. She has always been labelled a folk singer in the past, much to her annoyance. This is not a folk album. "Over the years I've got more and more interested in synthesised sounds," she explains. People have told her she shouldn't be: "'You're a naturalist. You can't be doing this.' Of course I'm not. I find it fascinating and since I was a child I've found it fascinating - how to record music. It's just wonderful now to be able to experiment and move out from what people's idea might be and not have to tailor what I do to what I think would be approved of."

Has she done that in the past? "I think with Lookaftering I was very aware that Diamond Day had become this sort of emblem of freedom and rural life, and that maybe I would upset people because that would be what was expected of me, to turn up with a horse and hitch it to a lamppost. And yes, I was always scared I would disappoint people."

It should be said Heartleap has all the qualities of her previous albums, though - a kind of delicate, filigreed sweetness; like clear water running over bare rocks. But her pride in its new textures is evident. "I've also been extremely lucky that I've been given the opportunity to spend time rather than being pressured like so many musicians. FatCat [her record label] gave me a deadline in 2008 and then another in 2010 and I sailed through them all. And they were really patient with me. My experience of coming back to the music industry - this terrible industry - has been fantastic."

In 2014, some 44 years after her first album was released, almost 50 years since her first single came out, Vashti Bunyan has arrived where she wants to be. It's been an eventful journey.

My father was a dentist and an inventor and an extraordinary man." Vashti Bunyan is telling me about her London childhood. "He had a laboratory in the house and it was such a completely typical mad professor's laboratory, with dusty bottles and bits of skeletons sticking out of cardboard boxes. A wonderful playground for someone like me. I was a very curious child. He taught me a lot. He taught me to dissect a frog. I had a very varied childhood. My mother tried to make us as respectable as possible and then, of course, I did the worst thing possible and went off with a scruffy art student and a horse and cart."

Bunyan was the youngest of three children but her older brother and sister were of a different generation. "My sister was a debutante in the last bunch of girls who were debutantes. And I had scruffy pigtails and I was in shorts and a T-shirt watching her practising her curtsey. Nothing would induce me to curtsey or wear a skirt."

The only music in the house was her father's classical music. He once bought an old piano which sounded dreadful, hadn't been tuned for years. Her mother found some sheet music and now and again Bunyan would spy on her playing and singing, "quite falteringly, but I could hear she had the most beautiful voice". Bunyan never let on that she was there, which she feels bad about now, but she's written a song about it. Was that side of her something she didn't want to display? "Or couldn't," Bunyan suggests. "Once she married my father that was it. People of her generation, mothers of her generation didn't have the choices I had. Or that I took, really. She had to be the dutiful mother and a dutiful wife."

That was never in Bunyan's plans. She spent her teens tuning in to Radio Luxembourg trying to hear the latest pop songs through the static and fade. Was liking that music a form of rebellion? "I wonder if it was. It could have been. I was sent to boarding school just before I was 15 and the night before I went I went to see Expresso Bongo." The Cliff Richard film in which Laurence Harvey plays a hustling manager looking for teenage talent to exploit? "Yes and I think that stayed with me all the torturous years of boarding school until I was finally allowed to leave and go to art school." Not that she applied herself greatly - music was by then the goal.

"That whole sleazy Soho pop music world was what I was incredibly drawn to and it was where I went looking for a manager, agent, anyone who would have me."

She found one in her late teens with Andrew Loog Oldham. It took a while. "I was a very scruffy individual and most girls of the time a) didn't write their own songs, b) didn't have a guitar slung over their shoulder and c) didn't have a holey jumper. I was knocking doors on Denmark Street and trying to find someone who might listen to my songs. Not particularly me, but my songs. And of course they were all patronising. Everybody would be patting me on the head. 'Very nice dear, but just not commercial.'"

She was singing at a friend's party when an agent saw her and thought of Loog Oldham. "Marianne Faithfull had just left him and she thought he needed a replacement." She went and sang for him. "He was extraordinary. He stood by the fireplace in this beautiful Italian suit with more makeup on than I had and he was just beautiful. I had a cold and sang my songs to him and I was sent out of the room. The next day I had a phone call to say he wanted to offer me a Stones song to record as my first single … And I was outraged. I wanted to record my own songs."

A compromise was reached. One of her songs appeared on the B side. But nobody paid attention to either. She made another single - Train Song - with a Canadian producer that got little airplay, then more recordings under Loog Oldham's watch, but they never saw the light of day. It all sent her into a "terrible nosedive".

Bunyan had met the "scruffy art student" Robert Lewis a few years before. Feeling she had to get out of London, the pair came up with the idea of travelling to Scotland in a horse and cart. They knew the Glasgow singer Donovan who had recently bought three islands near Skye and had the idea of setting up a community on one of them. Bunyan and Lewis decided they would travel there. It took them a year and a half (the community had been and gone by then).

It was not a happy, rainbow-coloured trip. At times people were hostile, taking them for Romanies. "There were many times in the journey that I felt: 'Why am I doing this? I'm cold, I'm hungry, we have no money, this is just crazy.' The thing that kept me going was the horse. What would we do with the horse if we stopped? We couldn't take her back to London. She was an old, old person. She was a wonderful creature. I think living like that, living with an animal, you become very bonded. Whether she was bonded to us you couldn't tell really. But we really loved her. She was part of our lives."

Halfway through the journey, Bunyan's mother died. "I could have gone back then and stayed with my father and looked after him, but he in fact went off to America and I just went back to the horse. And the boyfriend, I suppose."

While she was back in London for her mother's funeral she did meet the producer Joe Boyd and he offered to make an album with her at the end of the journey, as a document of her travels. "At that time only half the songs were written. He kept his word and a year later I went down to London to record. By that time I'd written songs like Jog Along Bess which he wasn't so keen on. He had liked the more romantic ones. But I had become so attached to the life and the journey and the animals and all of it that I was documenting them. And I think his heart sank. But he still kept his word and he made the album."

However, beyond Robert Kirby's arrangements Bunyan didn't like the result, positively hated the fiddle that was added to Jog Along Bess ("I love it now but at the time I was horrified"). Nobody else liked it much either. The album didn't sell and the reviews were terrible. "One was saying: 'It made me depressed.' The journey had been about getting away from depression - not that I knew that was what had been wrong with me - but that's how I got out of it. I remember reading this and thinking: 'This is terrible. I've just made somebody else depressed. I'm not doing that again.' And I didn't. I didn't pick up a guitar again until my son was 16 and I was teaching him to play."

There's that cussedness again. You can see it in the life she led in the years after, moving from place to place, only settling when her children were school age and building a "beautiful farm north of Glasgow". And in her commitment to a life outwith the norm, no matter how much that cost. She and Lewis never married. When she had her first child she was asked if she wanted him adopted as soon as he was born. "And then when my daughter was born nearly three years later I'd hardly even woken up and there was a social worker standing there saying: 'We'd like to offer you adoption for your child because two illegitimate children is two too many. And also, we'd like to offer you sterilisation.' And this was in 1973. I was horrified that I could be treated like that; that it was assumed I was an irresponsible person who wouldn't be able to look after my children because I wasn't married and didn't have a proper address - 'the Wagon'."

She laughs a lot telling her story. Even at the worst of it. She admits to a sense of failure when she and Lewis eventually separated, "because our lives had been the Diamond Day dream for all of those years and we had tried to make it a reality. But gradually I changed and I fell in love with my lawyer. We stitched together this amazing family and 22 years later we're still together."

Her kids grew up without music. There were maybe three tapes in the car, she says - Planxty, Bob Dylan and another she can't remember. They found their own way to it, of course, and to their mother's music. "I would never let them play Diamond Day. I'd make them turn it off." So they'd sneak out to the car to listen.

Others found their way to it too. The album had become a cult down the years. It was rereleased in 2000 to the sort of reviews Bunyan would have given her eye teeth for in 1970. By 2006 the title track was being used in a phone advert. The 19-year-old Vashti Bunyan would have loved that, she says. "All those people saying she wasn't commercial and then that song was made into a commercial. I know a lot of people were not pleased with me for allowing that to happen but it meant a lot to me for that word 'commercial'."

She smiles again. This is a story of vindication and a story about strength beneath the beauty. Fragile is not the word. n

Heartleap is out on FatCat Records on Monday.