Hagen's parents are Hans Hagen (also known as Hans Oliva), a scriptwriter, and Eva-Maria Hagen, an actress and singer. Her paternal Jewish grandparents died in Sachsenhausen concentration camp. Her parents divorced when she was two years old, and growing up she saw her father infrequently. At age four, she began to study ballet, and was considered an opera prodigy by the time she was nine.

When Hagen was 11, her mother married Wolf Biermann, an anti-establishment singer-songwriter. Biermann's political views influenced young Hagen: she was "dishonorably discharged" from the Free German Youth group at age 12, and became active in political protests against the socialist East German government.

Hagen left school at age 16, and joined the cover band Fritzens Dampferband (Fritz's Steamboat Band, together with Achim Mentzel and others). She added songs by Janis Joplin and Tina Turner to the "allowable" set lists during shows.

From 1972-3, Hagen enrolled in the crash-course performance program at The Central Studio for Light Music in East Berlin. Upon graduation, formed the band Automobil.

In East Germany, she performed with the band Automobil, becoming one of the country's best-known young stars. Her most famous song from the early part of her career was "Du hast den Farbfilm vergessen" ("You forgot the colour film") in 1974. However, her musical career in East Germany was cut short when she and her mother left the country in 1976, following the expulsion of her stepfather.

The circumstances surrounding the family's emigration were exceptional: Biermann was granted permission to perform a televised concert in Cologne, but denied permission to re-cross the border to his home country. During a period when bureaucracy was the norm, and families divided by the Berlin Wall had not seen one another in decades, Hagen submitted an application to leave the country.

In it, she claimed to be Biermann's biological daughter, and threatened to become the next Wolf Biermann if not allowed to rejoin her father. Just four days later her request was granted, and she settled in Hamburg, where she was signed to a CBS-affiliated record label.

Her label advised her to acclimate herself to Western culture through travel, and she arrived in London during the height of the punk rock movement. Hagen was quickly taken up by a circle that included The Slits and the Sex Pistols; Johnny Rotten was a particular admirer.