 He attended St Catherine's College, Oxford from 1958 to 1961, graduating with a BA degree.As a member of Oxford University Dramatic Society (OUDS), in 1959, Billington played the Priest in "The Birds", by Aristophanes, his only appearance as an actor, and, in 1960, he directed a production of Eugène Ionesco's "The Bald Prima Donna", a performance of which was attended by Harold Hobson, the drama critic for "The Sunday Times".Although it won "an Oxford drama competition" and was an entry in that year's National Student Drama Festival (NSDF 1960), which Hobson had co-founded in 1956, Billington's directorial debut was not well received at the Festival, yet Billington credits Hobson with having "changed my life."