Born in Derby in 1941 Ockendon attended Derby High School for Girls from 1946 to 1959. In 1959 she went up to read mathematics at St Hilda's College, Oxford. After graduating her first job was at GCHQ but after 2 years she obtained a research/teaching post at Somerville College and returned to Oxford. She completed her DPhil in 1968, and her dissertation, Relaxing Gas Flow, was supervised by David Spence.^[3]. She was then appointed to a permanent position as a Tutorial Fellow at Somerville and a lecturer at the University of Oxford, she held these positions until her retirement in 2008. Between 1988 and 1990 she was the Vice-Principal of Somerville^[4]: .

Between 1994 and 2002 Ockendon was the director^[5] of the Oxford Centre for Industrial and Applied Mathematics at the University of Oxford, where she is now an emerita member. She has been an Emeritus Fellow of Somerville College, Oxford since 2008.^[4] She was president of the European Consortium for Mathematics in Industry from 2001 to 2003.^[6]

She embarked on research in fluid mechanics but soon became involved in the Study Groups with Industry^[7] that were launched in Oxford in 1968 and since then much of her work has been driven by industrial problems.

The industrial problems she has worked on have come from a wide range of application areas but have mainly focussed on continuum models in fluids and solids. A particular area of interest has been the problems from the textile industry.^[4] She has also had a longstanding interest in nonlinear wave theory – both in fluids and solids. She was co-author of two textbooks on Fluid Mechanics^[8][9] both of which came out of lecture courses developed at Oxford.

Ockendon is the author of:

• Inviscid Fluid Flows (with Alan B. Taylor, Oxford University, 1972; Springer, 1983)^[8]
• Viscous Flow (with John Ockendon, Cambridge University Press, 1995)^[10]
• Waves and Compressible Flow (with John Ockendon, Springer, 2004; 2nd ed., 2015)^[9]

She has had a particular interest in promoting Industrial Mathematics in Europe via the European Consortium for Mathematics in Industry ^[6]: Council member (1998-2005), President (2001-2003), executive director (2012–15).

Honorary DSc, Southampton University, 1999.^[11]
Honorary member of ECMI since 2018.^[6]

Much of her research has been done in collaboration with her husband Professor John Ockendon.^[12]