It was founded in 1942 by and named after violinist Olive Zorian.

It gave the premiere performances of, and made the first recordings of, several compositions for string quartet by English composers, including Benjamin Britten and Michael Tippett.

It also gave the premiere English performances of quartets by Ernest Bloch and Béla Bartók.

[1] The original members were Olive Zorian (1916–65, violin I); Marjorie Lavers (violin II); Winifred Copperwheat (1905–76, viola); and Norina Semino (cello).

[5] The later date is supported by evidence that the violinist Frances Mason and the cellist Eleanor Warren were members of the Zorian Quartet in the 1950s.