PhD student Emma says she is tired of being called a "scrounger" by her friends and wants to make some money of her own.
She hopes to follow in the footsteps of her father, who shot to fame in the Sixties, and is about to release her first album.
Academic rebel
Speaking to Diane Madill on BBC Radio 4, Emma, 28, also said that her decision to study at Cambridge was an act of rebellion.
"Drink and drugs would not have been rebellion, would it? I think going to Cambridge was a rebellion," she said.
But now she is planning to give up her studies in history of science, and lecturing on her specialist area, the history of gardens.
Friends' jibes
She says she is tired of jibes about living off the taxpayer from her friends, who have all left university for high-paid jobs, houses and cars.
"They say: `Your research is totally obscure and I am paying for it with my taxes'."
Her parents, however, have always been "totally supportive" - except when she threatened to join the Army.
Army ambitions
"The one time my parents told me: `We really don't want you to do that,' was when I was doing Strategic Studies and I became convinced that what I wanted to do was go to Sandhurst.
"They said to me: `Please don't. Please don't join the Army."'
She has no qualms about trading on her famous name, especially since she follows not only her father, but many of her family, who were also musicians.
But her approach will be a world away from that of her dad, whose hell-raising antics and guitar-smashing on stage are part of rock folklore.
"I am doing something very different from what my dad did. I am not going to be smashing guitars," said the singer and pianist.