Bill Ashton remembers vividly the day an awkward 16-year-old girl by the name of Amy Winehouse turned up at his National Youth Jazz Orchestra. "The singing coach, Annabel Williams, came up to me after rehearsal and said: 'All she did was sit in the corner smoking for England – she didn't join in at all.'" He laughs. "But when it came to performing the song with the big band, she just got up and nailed it first time. Just from listening to the others do it."

A few months later, in June 2000, the NYJO staged a show at Rayner's Hotel in west London. Their singer dropped out at the last minute; Winehouse didn't know the songs, but wasn't fazed when Ashton called her. "She just said: 'Don't worry, I'll learn them on the train.' So between her stop in north London [Southgate] and Rayner's Lane, she learned all four songs on her Discman, and she sang them brilliantly. To do that is extraordinarily rare."

On the first anniversary of Winehouse's death, it's worth remembering just what a natural, instinctive musician she was. Her later, often shambolic shows (in particular that heartbreaking final performance in Belgrade) have gone some way to obscuring the memory of Winehouse at her best: she was one of the last decade's true superstars, a performer who could be strong, emotionally devastating, yet vulnerable, too. A 2006 appearance at the Other Voices festival in Dingle, which screens for the first time on BBC4 on Monday night, remains one of her most powerful: the singer is mesmerising as she interprets several songs from Back to Black over a stripped-back band.

Watch Amy Winehouse discuss her love of jazz and gospel music, and perform Tears Dry on Their Own at the Other Voices festival in 2006. BBC

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As a songwriter, she was compulsively biographical. "Everyone writes about their life, but her songs were so specific," says Tyler James, Amy's best friend since they met aged 13 at the Sylvia Young Theatre School. "Every line is about something that took place. I mean, she once wrote a song called Tyler in Cashmere just because she had an obsession with me wearing woolly jumpers." As teenagers, they would sing to each other on the phone. James says the bleak line "I cried for you on the kitchen floor" from You Know I'm No Good was inspired by one of many splits with her then boyfriend Blake Fielder-Civil. A 23-year-old Winehouse told the journalist John Kelly, who interviewed her at Other Voices, that she used to lie on her kitchen floor with a bottle of Jack Daniel's whenever she and Fielder-Civil broke up, playing the Shangri-Las' I Can Never Go Home Again on repeat: "I would pass out, wake up and do it again."

She grew up in a house filled with music. The television was rarely on, but even so silence was at a premium; as well as singing and tap-dancing, a young Winehouse would fill the house with the sound of her practising Home on the Range on a xylophone. Ashton thinks the biggest contributing factor to her talent was the fact that her father, Mitch, was a Jewish taxi driver. "They've got the best musical taste of anyone," he says. "They're extremely discerning, and their taste runs through very good singers. When NYJO did concerts at the Barbican, accompanying people like Buddy Greco, Rosemary Clooney or Peggy Lee, the entire audience was Jewish taxi drivers. Amy had that tradition, and what goes into your ears comes out of your mouth … it's as simple as that. The ear is the most important instrument of all. She had great ears." Her former bass player Dale Davis agrees: "She was into instrumentation and that came through in her voice. She had that ability to improvise phrases. She could sing the same song every night, but do it differently each time."

Winehouse herself talked to John Kelly about this, crediting not just her favourite jazz vocalist Sarah Vaughan for teaching her to sing, but also great instrumentalists such as Thelonious Monk. She likened Vaughan's vocals to the sound of a clarinet; her own vocals were coarser, more brassy. In Monday night's BBC4 documentary, Winehouse's sense of mastery and control is evident when she plays a song like Tears Dry on Their Own to a tiny crowd gathered in a Dingle church. Alex Feldman, former producer of the Radio 2 Soul Solutions show with Mica Paris, helped arrange Winehouse's first radio sessions, before the release of her debut album, Frank. He remembers a nervous, excited girl, overawed to be working with heroes such as Mica and Carleen Anderson.

"Her management exposed her to a select few radio people very early on," he recalls. "It was obvious straight away that we hadn't seen anything like her before. This was the first time I'd heard a British singer who had the whole jazz thing down, but who could also translate that into soul music." Feldman saw her perform around 20 times during this pre-Frank period, playing venues around London, from tiny members' clubs to bigger stages such as Bush Hall. "With a lot of showcases you'll go, watch it and say 'Seen that done.' But with her, you'd just go back and see her over and over again. It was fresh every time."

Of course, it wasn't just jazz that was played in the Winehouse household. Amy and her friend Juliette Ashby used to dress up as Wham! backing singers Pepsi and Shirlie, before forming their own rap group Sweet'n'Sour (Amy was Sour). Later, embarking on a love affair with R&B and hip-hop, Winehouse got into Missy Elliot, Nas, Faith Evans, Brandy and Monica. "The only thing we ever disagreed on was that she thought Monica was a better singer," recalls Tyler James. "I preferred Brandy."

Winehouse wrote her first song as a precocious 10-year-old, and learned to play guitar with James when she was a teenager. She also got better at songwriting: alongside a Beatles book (the two friends would jam on John Lennon's I'm Only Sleeping), she studied the basic chord diagrams and progressions from Carole King's Tapestry – "probably one of the best songwriters of all time, so it was a good place to start," says James. "We'd always sing So Far Away. That's my most memorable song of Amy's. That's what I had Mitch play at the funeral, because it was our song."

They went about writing in different ways. James wrote his music first. Winehouse would need to write "a whole page of lyrics" before she picked up a guitar to start building a melody for them. In his recent memoir Amy: My Daughter, her father Mitch describes the way she was always scribbling into a notebook, for reasons he was unaware of until he heard Frank. These lyrics were powerfully autobiographical, from tiny details such as punching "all the buzzers" on a door in Take the Box, to a cataclysmic event like her dad's affair (this formed the basis of What Is It About Men).

Everything was jotted down and saved for use at a later date. Winehouse was one of life's great observers, with a knack for selecting the right, cutting line. James still has her notebooks; he laughs as he recalls how every single page of her Back to Black notes features a drawing of a pin-up girl: "Massive hair, massive eyelashes – she was obsessed with them."

Back to Black, Winehouse's masterpiece, will undoubtedly stand the test of time; perfectly written songs don't go away. But even in those early, pre-Frank days – before the booze, the bad boys and the beehives – there were signs that she was not destined for the straight and narrow. Ashton remembers being surprised that the young girl who blurted her name at him when she first pitched up at the NYJO, and who then stood in a corner not speaking, also worked in a tattoo and piercing parlour. "She told me she was allowed to do minor piercings!" he laughs.

Even before she was signed, Winehouse could be self-destructive, failing to turn up to vital meetings with industry heads. "She had no desire to be famous, really," says James. "I don't think there was even a massive desire to be successful, beyond people liking what she'd done. She'd have been happy to do a gig at the Jazz Cafe [in London] once a month, and then work in a stall in Camden and play pool. Some people are really driven in terms of wanting to be successful, but Amy was driven by a passion for music."

That passion was undoubtedly the key to her great success. On the application form Winehouse filled in for the Sylvia Young theatre school, aged 12 (without telling her parents), she wrote: "I want people to hear my voice and forget their troubles for five minutes." It was something she spent her life doing, before she turned towards more destructive forms of escape. It tells you something about why her music connected, and still connects. Here was someone who knew the redemptive power of music – who was not just a naturally gifted musician, but also a true music fan.

• Amy Winehouse: The Day She Came to Dingle, an Arena documentary for BBC4, will be broadcast at 10pm on Monday 23 July

• The Amy Winehouse Foundation will be Ebay's charity of the week between July 23 - 29. For info got to amywinehousefoundation.org



• This article was amended on 23 July 2012. The original said that Amy Winehouse's final show was in Ukraine. This has been corrected.