Kumar was born in Haridwar, Uttar Pradesh, India, to Jagat Ram Saini and Santosh Kumari, who emigrated to Derby when he was twelve years of age. He attended Rykneld Secondary Modern School, Derby. He left at 15 to study for O-levels at Wilmorton College, and attended Derby & District College of Art & Technologyfor his 'A' Levels. He then studied chemical engineering at Aston University, Birmingham where he was awarded a BSc in 1978, and an MSc in Process Analysis and Control Theory in 1980, and a PhD in Fluid Mechanics in 1982. The thesis title was Velocity distributions in a plate heat exchanger. He was a Fellow of the Institution of Chemical Engineers, a Chartered Engineer and a Member of the Energy Institute.
He was a Research Fellow at Imperial College London (1982–5) and worked as a research scientist at British Steel Corporation in Middlesbrough from 1985 to 1997.
He began his political career as a local councillor for Middlesbrough Borough Council (1987–97). He became the MP for Langbaurgh at the 1991 Langbaurgh by-election, but lost the seat to the Conservative candidate in the 1992 election. He won Middlesbrough South and East Cleveland at the 1997 election, and held it until his death in 2010.
He was a Member of the Parliamentary and Scientific Committee; Vice-Chair of Parliamentary Group for Energy Studies; Chair of the Parliamentary Office of Science and Technology (POST); and Chair of Northern Group of Labour MPs.
In June 2010 IChemE (the Institution of Chemical Engineers) and NEPIC (the Northeast of England Process Industry Cluster) launched the Ashok Kumar fellowship at POST in memory of Kumar. The annual fellowship will see the successful candidate spend three months at the Parliamentary Office for Science and Technology (POST). By 2017 the 6th Ashok Kumar Fellow had been appointed to work with POST she was a postgraduate engineering student, Erin Johnson, from Imperial College, London.
Ashok Kumar MP was a supporter of industrial engagement and the concepts of economic clusters. He regularly chaired the NEPIC MP/Industry meetings and contributed to the growth and innovation agenda of the Cluster. Tributes from NEPIC Industrialists for his work came after his untimely death.
Ashok Kumar was a Distinguished Supporter of the British Humanist Association and supported the Labour Friends of Israel. Of Hindu and Sikh descent, he described himself as a lifelong "liberal humanist". He listed his recreations as "Cricket, badminton, reading history and philosophy, listening to jazz". Aston University gave him an honorary degree in July 1997.
Kumar never married. He lived in Marton, Middlesbrough.
Kumar was found dead by police in his constituency home in Canberra Road, Marton on 15 March 2010. Police announced that he had died from natural causes.