Burns spent much of her career on stage, beginning in London in the 1940s (including a stint with the Royal Shakespeare Company in 1947, with Paul Scofield and Donald Sinden). During this time, she was heard often on BBC radio, including a 1948 serial of Emma and reading serialized novels (Wilkie Collins' Poor Miss Finch for two months on Woman's Hour in 1952). Married to stage producer/director Michael Langham until his death, Burns is the mother of Chris Langham.