In 1954 she married her professional colleague Gunnar Möller with whom she was seen in the same year in the music movie Love and Trumpets.
In the TV series Die Gäste des Felix Hechinger (directed by Rolf von Sydow) Brigitte Rau played the role of Monika Lenz, in the series part Ehe in Gefahr her husband played her husband Peter Lenz.
In the 1970s, Gunnar Möller and Brigitte Rau appeared predominantly together in theatre productions, among others also at the Landesbühne Hannover.
In 1977 they both appeared on stage in Heinz Coubier's comedy Aimée directed by Helmut Käutner.
The family had previously changed residence several times before settling in the Hampstead district of London's artists.