Born to an upper-class family that had to flee Montenegro after the German and Austro-Hungarian occupation in 1916, Plamenatz came to England as a boy and was raised there.
His father Peter was a politician active in the True People's Party and served for one term as a Foreign Minister for Montenegro, while his mother was of aristocratic background.
He was educated at Clayesmore School, whose head master and founder, Alexander Devine, was an activist for the Montenegrin cause, and at Oriel College, Oxford, where he read history.
Plamenatz's speciality was political theory, which he spent most of his academic life teaching at the University of Oxford.
He returned to All Souls as a professorial Fellow in 1967 when he succeeded Isaiah Berlin as Chichele Professor of Social and Political Theory.