Styrene, whose real name was Marion Elliott-Said, had been suffering from cancer.
A statement on the singer's official website and Twitter feed said Tuesday that "the beautiful Poly Styrene, who has been a true fighter, won her battle on Monday evening to go to higher places."
Video: X-Ray Spex, "Oh Bondage! Up Yours!"
Boy George was among those paying tribute on Twitter, writing, "Oh bless you Poly you will be missed! Legend!"
X-Ray Spex released just one album, 1978's "Germ Free Adolescents." But its aggressively catchy single "Oh Bondage, Up Yours!" became an enduring punk anthem.
Styrene later said the song - a gleeful nonconformist shout-out - was inspired by the iconic bondage trousers designed by Vivienne Westwood.
"Some people think that little girls should be seen and not heard," Styrene sang - before letting everyone know exactly what she thought of that idea.
Of British and Somali heritage, Styrene was born in 1957 in the London suburb of Bromley - a quiet corner backwater with a strong rock 'n' roll streak that was also the childhood home of David Bowie, Billy Idol and Siouxsie Sioux.
As a teenager she released a reggae single before being inspired to form a punk band after seeing the Sex Pistols play in 1976. X-Ray Spex stood out from the punk crowd during its short career, both because of its female singer and for including a saxophone player in the lineup.
Styrene's attitude and energy inspired other female singers, and she was often cited as a precursor of the 1990s "riot grrrl" movement.
Styrene later joined the Hare Krishna movement and released several solo albums - the most recent, "Generation Indigo," just last month.
She told the BBC in an interview she would like to be remembered for something spiritual, but "I know I'll probably be remembered for 'Oh Bondage, Up Yours!'"
Earlier this year she revealed she was battling breast cancer that had spread to her spine and lungs, but said she hoped to overcome the disease through a combination of conventional medicine and alternative remedies.
She is survived by her daughter, Celeste Bell-Dos Santos, who fronts the band Debutant Disco.