Wise Children by Angela Carter

Dora and Nora Chance are a famous song-and-dance team of the British music halls. Billed as The Lucky Chances, the sisters are the illegitimate and unacknowledged daughters of Sir Melchior Hazard, the greatest Shakespearean actor of his day.
 
A richly comic tale of the tangled fortunes of two theatrical families, the Hazards and the Chances, Angela Carter's witty and bawdy novel is populated with as many sets of twins, and mistaken identities as any Shakespeare comedy, and celebrates the magic of over a century of show business.