During his ten years in the British army (which included a spell as an intelligence officer in West Berlin), Glenny earned his Master's degree in Modern Languages followed by postgraduate study in Soviet studies at Oxford University. He left the army in 1954 to go into business. As a salesman for the Wedgwood company he first visited the Soviet Union. In 1964 he joined The Observer newspaper in London as a reporter, but left three years later.

Glenny was a lecturer in Russian language, literature and history at Birmingham University (1969-75), Southern Illinois University (1975-77), and Bristol University (1977-84).

He was the author of several works on Russian literature as well as co-author with Norman Stone of The Other Russia, an oral history of the experiences of Russian emigres for which he also conducted many of the interviews.

Glenny's numerous translations included works by Nikolai Gogol, Fyodor Dostoevsky, Maxim Gorky, Mikhail Bulgakov and Aleksandr Solzhenitsyn, as well as the first volume of Boris Yeltsin's memoirs.

His son Misha Glenny is a writer and broadcaster on eastern Europe, particularly the former Yugoslavia.