After the war her family moved to Hampstead and eventually settled in Shoreham in Kent from where she attended Tonbridge Grammar School. Her writing career started with her winning a poetry competition in the Daily Mirror at age 16. Leaving school her first publication was a volume of two novellas, Dust Falls on Eugene Schlumburger/Toddler on the Run the following year.

She holds a Fellowship of the Royal Society of Literature and is also Honorary Visiting Professor at Middlesex University. In an interview with The Telegraph in 2004 Shena explained that she is synaesthetic and "sees words as colours", her own name is yellow.