Penned by Matt King and Oliver Lansley, the kitchen-based comedy also starred Isy Suttie, Darren Boyd and Katherine Parkinson.
According to the British Comedy Guide, the show may have been a victim of cuts in the BBC Comedy department.
Responding to the news on Twitter, Davies described the axing as the "worst news I've had in my whole career". Peep Show star Suttie added: "Just heard our BBC Two series Whites has been cancelled. I am so sad. Thanks so much to everyone who watched and supported the show."