Had anyone ever asked the Sixties star to pen her life story, they would have unveiled an astonishing tale of love and loss a thousand times more remarkable than that of former teen pop star Billie.
While Billie recalls the details of her relatively brief life, Anneke is living like a hermit in a remote two-bedroom cottage on the edge of Dartmoor.
As she puts it: 'My heart has been broken several times.
I have always been attracted to men who are extremely talented, beautiful and absolute b******s.' From the start, Anneke's life was like something out of a film.
The daughter of a Dutch-born Parisian catwalk model and a Harrow-educated artist descended from Elizabethan sea lord Sir Richard Grenville, she was born in 1941 in a private nursing home near Pinewood Studios.
Her parents Anna and Alaric Willys (she later changed her name to Wills) had planned to buy a little house in the South of France but war in Europe put a stop to that.
They both won over fans of the sci-fiseries with their blonde hair and thick dark lashes.She adds: 'I remember looking in the mirror afterwards to see if I looked any different. But Edward Fox, a year above her at Rada, was the first to steal her heart.Their relationship and her wilful attitude to staff resulted in her being asked to leave.Life never quite turns out as you expect it.' Anyone seeing the reclusive, bespectacled silver blonde woman pottering around her local Devonshire village would find it hard to believe that in her day, Anneke was at the zenith of 1960s celebrity London.Or that she was thrown out of Rada at 17 for 'behaving badly' with Edward Fox. In a quiet corner of her garden, she has a bathtub set beneath a canopy of trees which is connected up to the kitchen sink by a hose.
Or that at just 18 she was pregnant with Anthony Newley's child and forced to abort it when he left her for Joan Collins. On summer mornings, she lies in the warm water, taking in the glorious view across the moors and reflecting on the astonishing events of her life.