Martha's famous for appearing on stage in her lingerie, something for which Tallulah Bankhead famously scandalized London in the 1920s, though she's not mentioned in the show.
Some of the movie and theater stars of the day mentioned are Ivor Novello, Jessie Matthews, John Gilbert, Douglas Fairbanks, Mary Pickford, Marion Davies, Lillian Gish, Rudolph Valentino, Noël Coward, Gerald du Maurier, and Ivy Duke.
Charles Brett wants to buy a Daimler but ends up buying an Austin.