He was born in London to a family of Jewish immigrants escaping from the Russian empire. After college and national service, he took the Russian course at the Joint Services School for Linguists, in Cambridge and Bodmin, Cornwall. Afterwards, he went on to study Russian and Serbo-Croat at the University of Nottingham, gaining a first-class degree. He received his PhD from Oxford University, his topic being the Jewish Labour Bund. Having completed his doctorate entitled The relations between the Jewish Bund and the RSDRP, 1897-1903 in 1960, he took up an academic career at Oxford where he eventually became the director of the Russian centre at St Antony's College. He retired in 1998.
He was married twice. His first wife was Ann King-Farlow, also a Russian scholar, and his second wife Barbara Jacobs, an artist. His son Henry Shukman is a travel writer and novelist. Another son David Shukman is a science journalist.