He was born in Vienna, but emigrated with his family to London in 1938 after Hitler's Anschluss.

During a brief internment as an enemy alien on the Isle of Mann, he met Austrian violinist Peter Schildhof. After the war, Brainin and Schildhof formed the Amadeus Quartet—first known as the Brainin Quartet, and then as the London Vienna Quartet—along with violinist Siegmund Nissel, who was also in the internment camps, and cellist Martin Lovett. (For the quartet, Schildhof transformed himself into a violist.)

The ensemble, known for its performances of Schubert and Britten, made its Wigmore Hall debut in 1948, but was already so well known that hundreds of people were turned away. The quartet eventually became one of the most-recorded string quartets in history.

The group disbanded after Schildhof's death in 1987.