Death in White Pyjamas

Here are the ingredients of the plot.
SCENE : Sam Richardson's country house.
CHARACTERS - Sam himself, a kindly business man, more amiable than artistic.
Basil Barnes, his producer, tall, slender, sleek-haired and slightly sinister.
Willy Farnham, a grand old character actor, always hard up,
Angela Walsh, a brilliant young Ingenue from the Provinces.
Deirdre Lehaye, tall, dark, icy, and so dead sure of herself that most men were scared to approach her.
Clara Maddison, the company's most tried and trying actress.
Rudolph Millar, her nephew, a rising young playwright.
That's the set-up. Deirdre Lehaye is murdered. Who did it? And why was she in white pyjamas?