Millennials might recognise Brix Smith-Start as a presenter on television's Ultimate Shopper and Gok's Fashion Fix. Gen Xers might have met her at Start, the pioneering boutiques she and husband Philip Start opened in Shoreditch.

To music fans, she will always be the woman who helped transform The Fall - arguably one of Britain's most influential bands - from a sour, image-averse boys' club to a shape-shifting group skirting fashion, pop, and something like stardom.

But Smith-Start's origins, as she reveals in her new autobiography, The Rise and The Fall and The Rise, might surprise even hardcore fans of The Fall, which is still kicking after 35 years.

Smith-Start was born Laura Elisse Salenger to a moneyed Los Angeles family whose Yiddish-speaking patriarch had emigrated from Russia via Ellis Island. Through wealth built on murky real-estate deals and the invention of the automated car wash, he and his wife became fixtures in LA's A-list social scene.

"In this country, a lot of people know who I am, but have no idea who I am," says Start-Smith from the Shoreditch loft she shares with her husband and pugs Gladys and Pixie.

"I've been quiet about a lot of personal stuff. There are stories in there I hadn't even told my husband."

Some of her book's most evocative passages recall Sundays at LA's Friars' Club, where Hollywood's Jewish elite would gorge from seemingly endless platters of food - "French toast, pancakes, waffles, bacon, sausages, omelettes, and an odd collection of Jewish delicacies like noodle kugel, knish and matzo-ball soup," she recalls. In one passage, Smith-Start tells of meeting Milton Berle at an adjacent table.

"When we walked away, I heard my grandfather mutter snidely under his breath, 'His face is so tight it looks more like his tuchas.'"

Smith-Start's grandparents, Oscar and Ethel Salenger, emerge as fascinating characters, present in her life, but mysterious and somehow out of reach.

They play as formative a role as her mother Lucy, a globe-trotting broadcast executive, and her father Steve, whose sanity unravels as the book progresses.

"My grandparents represent the whole notion of family for me, and of generations coming together," she says. "They were great storytellers. I loved my grandfather's stories about leaving Russia, coming to America, to Ellis Island, impoverished. He was a real Jewish-American success story. We learned so much about history, and the history of the Jewish people. There was a real sense of where we came from. Traditional family holidays like Passover were also major events. I even loved Yom Kippur. And Chanucah was great, I got presents every day."

After moving to Chicago with her divorced mother, Smith-Start fell in with a clique of teen punks. Her obsession with The Clash's The Guns of Brixton earned her the nickname Brixton, later clipped to Brix.

A chance meeting with Fall founder Mark E. Smith after a Chicago performance - as she tells it, they literally bumped into each other - led to a whirlwind romance, a move to Prestwich, Manchester, and marriage.

The North was a rude awakening for the Jewish kid from Beverly Hills. "Glowering Victorian red-brick buildings lined the sides of the streets. They looked like mean structures, where horrible atrocities had been committed in decades past," she writes in The Rise, The Fall, and The Rise. "The sky was toxic; the few people I saw seemed joyless."

She worked her way up in The Fall, gaining grudging admiration from bandmates – but scorn from some of the music press and even fans.

"Everyone was suspicious," she said. "I was the blonde American girlfriend. They thought it was nepotism. But once we started releasing albums with songs I had written, journalists and fans started realising I was a writer, and that I was bringing something to the table. I wasn't just a blonde pretty girl holding a guitar. People are now talking about the Brix period as the most commercially successful and fertile, how it brought in so many people, how I can write a riff and a hook."

Smith-Start's tenure in the band ended as her marriage to Smith disintegrated; perpetually drunk and addicted to speed, Mark E. Smith was also managing multiple mistresses while Smith-Start waited at the dinner table over cold plates in their Prestwich flat.

After the couple's disastrous mid-'90s split, she quit the rocker lifestyle, waitressed in LA, lived in the garage of Bangles' frontwoman Susannah Hoffs, romped with violinist Nigel Kennedy and poet Murray Lachlan-Young, and finally settled down with Start, founder of menswear retailer Woodhouse. Her own, hard-fought success followed in fashion and broadcasting.

Only now is Smith-Start being acknowledged for her centre-stage role in the Fall. Indeed, "as a female musician, she was still something of a rarity," says David Simpson, author of The Fallen: Life in and Out of Britain's Most Insane Group (Canongate, £10.99). "You can hear her impact in the sound - which gradually transforms from her entrance circa [1982's] Perverted By Language to a career classic such as [1985's] This Nation's Saving Grace.

Smith-Start "is all over that album," Simpson says. "She brought a poppier, more commercial sensibility, some great, twangy riffs and an element of style to a band that had always been anti-fashion with no image whatsoever beyond that of ordinary English working males."

A couple of years ago, Smith-Start reunited with old Fall bandmates as Brix & The Extricated, playing some of the songs she co-wrote for the first time in three decades. At their first gig, when they played the classic Hotel Bloedel, audience members wept. Her new band continues to tour; if YouTube footage of recent shows is any indication, they're ripping through Fall classics with even more fury and crunch.

Though it wasn't her intention, The Rise and The Fall and The Rise also offers a kind of secret Jewish history of The Fall, whose abrasive tunes might include cryptic non-sequiturs like "Jew on a motorbike!" Or imagine the Israeli capture of Nazi Martin Bormann.

"Mark is very widely read and has a particular fascination for the Second World War/Nazi Germany," says Simpson. "Also, Mark is of the post-war generation whose parents went through it, so it was relatively close. He also lived in a Jewish area, so will perhaps have been particularly struck by the events of 1930-45."

Smith-Start, however, has a different take on her ex-husband. "Mark loved Jewish women!" Smith-Start says. "He thought they were really sexy. He loved Jewish people. Our neighbourhood, Prestwich, was and is a Jewish neighbourhood. He was really tolerant of lots of things." That doesn't square with the shrivelled Mark E. Smith who made disparaging comments about refugees in Manchester in a BBC interview this year, Smith-Start is told.

"I have no idea nor do I care what he's saying now. I don't want those thoughts invading my body," she retorts.

Did she ever consider hiding her background when she moved to the UK?

"I was a little concerned. I came from a very different background than [the band] came from. I didn't want them to think I was privileged and playing at something," she recalls. "But I'm a grafter, utterly professional. They saw my work ethic, the passion. The background stuff evaporated."

Today, she says, "Judaism is part of who I am. I'm very open spiritually to lots of different things. I accept and feel there's a place for every religion. Whatever works for people is OK by me," she says.

"I am a Jew. My blood is Jewish. If anyone asks, that what I am."

Brix Start Smith is speaking at the Edinburgh Book Festival on August 20. Her book is The Rise, The Fall, and the Rise (Faber & Faber £14.99)