Sotheby's says the 1932 painting, called "La Lecture," was bought by an anonymous buyer over the phone after some six minutes of heated contest among bidders.
The painting was expected to fetch up to 18 million pounds ($28.9 million). The picture's selling price Tuesday included a premium of 2.7 million pounds ($4.3 million).
It shows Walter, Picasso's mistress and model for several paintings, asleep in an armchair.
Walter was 17 when she met Picasso, and she later had a daughter, Maya, with the artist.