Born in Vadodara, Desai grew up with his four siblings — two brothers and two sisters. He went straight to secondary school at the age of five, matriculated at 14, was an Honours student before he was 18, had a master’s degree before age 20, and a PhD at age 22.
After he secured a master's degree from the Mumbai School of Economics (then Bombay School of Economics), his parents wanted him to become an IAS officer. But the qualifying age was 21, and he was still 19. In between, he won a scholarship to University of Pennsylvania. He left India in August 1960 to move to the US.
Desai has written extensively on a wide range of subjects. From 1984-1991, he was co-editor of the Journal of Applied Economics. He has been both Chair and President of Islington South and Finsbury Constituency Labour Party in London and was made a life peer as Baron Desai, of St Clement Danes in the City of Westminster, in April 1991.
In 2002 Lord Desai wrote a book Marx's Revenge: The Resurgence of Capitalism and the Death of Statist Socialism which states that globalization would tend toward the revival of socialism. He published a biography of Indian film star Dilip Kumar titled, "Nehru's Hero: Dilip Kumar in the life of India" (Roli, 2004). He has described the book as his 'greatest achievement'. Examining Kumar's films – some of which Desai has seen more than 15 times – he discovers parallels between the socio-political arena in India and its reflection on screen. He discusses issues as varied as censorship, the iconic values of Indian machismo, cultural identity and secularism, and analyses how the films portrayed a changing India at that time.
During the course of writing this book he met Kishwar Ahluwalia, his second wife who worked as an editor for this book. On July 20, 2004 he married Ahluwalia. Desai, then 64, and 47-year-old Ahluwalia, were both divorcees and married at a registrar's office in London.
In 2005 he retired as Director of the Centre for the Study of Global Governance, which he founded in 1992 at LSE, where he is now Professor Emeritus. He is Chairman of the Trustee's Board for Training for Life, Chairman of the Management Board of City Roads and on the Board of Tribune magazine. He is an Honorary Associate of the National Secular Society.