John Lennon has proved to be a tough act for his sons Sean, centre, and Julian to follow.

In 1994, there could be little doubt about whose son he was. Heralded as one of the shining talents of the decade, he had the same astonishing vocal range, an equally impressive guitar-playing gift and a similar melancholy in his approach to songwriting. Then last year, he followed his father to an early grave, drowning in a freak accident in the Mississippi. He was only 30.

Inevitably, there have been some rebels in the rock’n’roll dynasties – children who, despite having names that sound designed for album covers, have opted for a more conventional life (by their parents’ standards, anyway). Jade Jagger (daughter of Mick) is in the fashion business, Moon Unit Zappa is an actress and Scarlett Page (daughter of Led Zeppelin’s Jimmy Page) is a photographer.

Zowie Bowie (son of David) even changed his name to the less spectacular Joe Jones. Emma Townshend is unimpressed. ‘Me and my sister used to say, “Mother! How could you call us these boring names?” Especially me, because my sister’s called Arminta. We used to go to gigs and we’d see Jade Jagger hanging out with Zowie Bowie and we decided we should have been called Tinsel and Tamla Mo Townshend.’

Of course, if you do carry the genes and the name of someone idolised by millions, simply opting for another career is unlikely to shield you from envy and accusations of nepotism, as the furore over the appointment of Stella McCartney as chief designer for the House of Chloe proved.

Headlines such as ‘All You Need Is Dad’ accompanied harsh quotes from mocking pundits. Former Chloe designer Karl Lagerfeld said, ‘I think they should have taken a big name. They did – but in music, not fashion.’

Her father, Paul McCartney, is having none of it. ‘People may envy her for getting the job, fine, but there are better paid jobs in the world and boy, she’s gotta deliver. There’s no way she gets away with it. And she’s aware of that. My kids got this from the age of five. There was no shelter for them. Kids used to follow them round the playground singing Mull of Kintyre, and they had to learn to turn round sharply and have an answer. So they’ve kind of lived with it. But hey, you’re talking to a proud dad here. My kids are the best in the world. They’re sensational.’

Emma Townshend reports that her father always encouraged her to become a musician. You might expect a little resistance from loving parents contemplating their children entering a trade known for its association with sex, drugs and debauchery. Does Pete Townshend, a reformed heroin addict and alcoholic, really think this is any sort of life for his daughter?

‘Emma has always been a bit of a star in the family,’ according to Townshend senior. ‘One of my cherished memories was a pushchair walk through a local park. She was mischievously wearing rock star sunglasses at two years old, but in the deadpan manner of a retired theatrical dame rather than a showbiz celebrity.’

He is full of praise for her music, which he finds intelligent, challenging and sometimes disturbing, even, at one point, using the word ‘genius’. He does not, however, take all the credit, commenting that her songwriting draws as much from her mother’s side of the family: Emma’s grandfather, John Astley, was a television and film composer; her uncle, Jon Astley, is a producer; and her aunt, Virginia Astley, a solo recording artist. ‘I believe she will be successful because she is so alive, so interested in the world,’ Townshend says.

Paul McCartney professes to be sanguine about the whole business. ‘People say to me, “Are the kids musical?” and I know what they mean. They mean, “Can we expect to see them on the stage shortly?” I always said I would never push the kids into showbiz and I never have. But James is a musician and would like to do music. I constantly talk to him and say, “You know, don’t you, what they’re going to do the first time they hear anything? You know you’ll be directly compared?” He says, “It’s cool, you’re my dad, you did that, it’s good. I don’t think I have to compete.” I think he’s got a level-headed view of it. What are you gonna do if it’s in your genes?’

McCartney laughs. As far as he is concerned there is only one solution: ‘Obviously if you’re a celebrity you just shouldn’t have children.’