Kumar Bhattacharyya was born in Bangalore, the elder son of Sudhir Kumar Bhattacharyya (1909-1987) and Hemanalini Chakraborty. Of Bengali origin, the Bhattacharyyas were a zamindari family from Dhaka District (then in the Bengal Presidency of British India and now in Bangladesh). At the time, his father, a distinguished professor of physical chemistry and subsequently Fellow of the Indian National Science Academy, was a professor at the Indian Institute of Science in Bangalore, where Bhattacharyya spent the first 12 years of his life. In 1952, upon his father's appointment as head of the chemistry department at the new Indian Institute of Technology, Kharagpur, the family moved to Kharagpur.

Bhattacharyya studied Mechanical Engineering at the Indian Institute of Technology, Kharagpur, taking his degree in 1960. The following year, he moved to Britain where he worked for six years as a graduate apprentice at Lucas Industries, a large British Manufacturing company. During this time, he studied at the University of Birmingham where he attained an MSc in Engineering Production and Management and a PhD in Engineering Production. While completing his PhD at Birmingham, he was appointed as a Lecturer and began the process of establishing a Manufacturing education programme for industry there.

In 1980 he moved to the University of Warwick and, with the support of Vice-Chancellor, Jack Butterworth, he founded WMG (Warwick Manufacturing Group) of which he is now chairman. WMG is now one of the largest academic departments of the University known for its collaborative research and education programmes with industry. During this time, he has been instrumental in brokering some significant partnerships for UK Manufacturing including the takeover of Jaguar Land Rover by Indian firm Tata Motors in 2008 and the investment in the National Automotive Innovation Centre at the University of Warwick.

Kumar Bhattacharyya is a past member of the UK Council for Science and Technology and a past board member of Advantage West Midlands, the West Midlands Regional Development Agency (RDA). He has also served as a scientific adviser to the government of South Africa. He sits on the Policy Advisory Council of the Institute for Public Policy Research and served on the National Consumer Council from 1990 to 1993.

In 2002, Andrew Lorenz wrote a book about Bhattacharyya's career and the growth of WMG, entitled Kumar Bhattacharyya: The Unsung Guru.

Bhattacharyya was appointed a Commander of the Order of the British Empire (CBE) in the 1997 New Year Honours and knighted in 2003. On 3 June 2004, he was created a life peer as Baron Bhattacharyya, of Moseley in the County of West Midlands. He sits on the Labour benches in the House of Lords.

In 2014, he was elected as a Fellow of The Royal Society. He is also a Fellow of the Royal Academy of Engineering and a number of other professional bodies including the Institution of Engineering and Technology, Institution of Mechanical Engineers, Indian National Academy of Engineering and the Chartered Institute of Logistics and Transport.

In 2016 Prime Minister Theresa May visited WMG with Chancellor Philip Hammond as part of her government’s development of a UK Industrial Strategy.