The classical pianist James Rhodes treats people who approach him in the street with a smile, a shrug, an excitable patter that exudes familiarity and warmth. Cab drivers enquire about future concerts, pensioners doff their caps, and baristas compliment him on his YouTube presence.

Four years ago, this articulate musician was in a mental hospital, where he made suicide attempts after years of sexual and drug abuse. He had quit his job in finance and gone through a divorce.

Last March, he became the first classical pianist to be signed by a major rock label and now he has released the first of six albums made with Warner Bros Records.

Being an overnight success is one thing; going from rock bottom to becoming the poster boy for a genre is quite another. "If I go into a… department store and I want to buy classical music they send you down to the basement like you're buying dodgy porn," he says. "Every single album has a cover that's an 18th-century French watercolour with a disturbed-looking player with tails on the back of the sleeve. They look the same. I wouldn't know where to start."

Rhodes has the antidote. He brings an informality to his performances, engages with his audience and wears sports jeans and a tee-shirt in place of a stiff collar and tails. He might intersperse Debussy and Grieg with anecdotes about pop culture, and reads music from an iPad propped up on his piano.

His relaxed attitude is atypical of this sometimes stuffy art form, though his past fits another stereotype: that of the gifted musician with a tortured soul.

Rhodes' biography makes difficult reading. Born to a middle-class Jewish family from St John's Wood, London, in 1975, he felt isolated from his friends and family while growing up, exacerbating the impact of the sexual abuse he experienced at school. As a teenager, he experimented with drugs ("weed, and more", he says). The abuse landed him in hospital with back injuries.

While Rhodes talks freely about his troubled life, he is just as focused on moving on. "Recently I had a victimhood moment,"he says. "But then I wake up and think I should stop crucify­ing myself. The sexual abuse, the breakdowns, the drugs, the suicide attempts – I am comfortable with all of it belonging in the past. It's not something to dwell on. The truth about that stuff, especially the sexual abuse, is that I don't need to hide, they are the ones who need to hide. If we shut up, then they won't."

Through it all, Rhodes always had music. Aged seven, he fell in love with Beethoven's Emperor concerto, and started playing piano. Aged 18, he was offered a scholarship at the Guildhall School of Music & Drama, though studied psychology at university because of pressure from his father.

Then life took over and he stopped playing completely between 18 and 28, when he worked as a sales director for a London financial publisher. He had a son, Eddie, who now lives in America and whom he sees "three or four times a year" after divorce from Eddie's mother, whom he identifies only as an "American Catholic writer".

And then he had a change of heart. "Part of the reason I pursued piano was that Eddie asked me why I wasn't doing it." But the pressure to succeed took its toll. In 2006 he was sectioned to a London psychiatric hospital for symptoms including depression and trauma.

"It was a combination of stuff, stuff from the past I hadn't dealt with, and then losing the safety net of a stable career, the marriage ended," he said. "It's a scary thing to do. I think I've done a kind of reverse Amy Winehouse, I might even cut my hair soon."

Tuition from the Verona pianist Franco Panozzo, agent to the legendary Russian concert pianist Grigory Sokolov, led to Rhodes' first two albums, 2009's Razor Blades, Little Pills and Big Pianos and Now Would All Freudians Please Stand Aside, released last March by the independent Signum Records. Each went to the top of the iTunes chart. "The format was very much like a piano recital but I want to reach as many people as possible," he says.

His new album, Bullets and Lullabies, is a double CD: one disc the pacier work of Ravel and Chopin; the other slower pieces by Chopin and Brahms. "I wanted it to be 24 hours in my life," Rhodes says. "You get up and it's immediately 100 miles per hour with thousands of notes flying around, you sit at the piano and you work and you get on the Tube and it's all manic and noisy. Walk down [the] street, go see the shrink. And then the lullabies. You get home at five o'clock, you're running a bath, you're trying to wind down, it's just more Valium music. You get into bed and you fall asleep to it."

His own TV series about classical music, James Rhodes: Piano Man, has been re-running on Sky Arts and if he has his way, piano playing will never again be labelled as staid. "These famous composers were real players," Rhodes says. "Bach had 21 children. I want people to know he wasn't this dour guy."

Bullets and Lullabies is out now