The Phoenix and the Carpet by Edith Nesbit

From Robert, Anthea, Jane and Cyril's new nursery carpet there falls a mysterious egg which is hatched in the fire to reveal a benevolent, resourceful and ingenious Phoenix who explains that the carpet is possessed of magic qualities.

And so begins a series of fantastic and bizarre adventures as the carpet transports the children and the Phoenix to places as diverse as a chilling French castle, a desert island and even the Phoenix Fire Insurance Company's offices, which the Phoenix believes to be a shrine for his followers.