He was the elder identical twin brother of Alec Bedser (1918–2010), widely regarded as one of England's top bowlers of the 20th century.

Eric Bedser was born in Reading, Berkshire 10 minutes before his twin brother Alec.

There is a famous story that when Eric and Alec were first selected for Surrey, they agreed they couldn't both be fast bowlers, as at that time they were.

A flip of the coin saw Alec win the toss, and Eric consequently took up off-spin bowling, at which he became very adept in a Surrey county team that was dominated by famous spinners such as Jim Laker and Tony Lock, and concentrated on his batting.

Among other business interests, they co-operated with Ronald Straker in a successful stationery firm, Straker-Bedser, which was later taken over by Ryman in 1977.