The impressionist's 1932 piece, Femme Assise Pres d'une Fenetre (Woman Sitting Near a Window), is a portrait of his "golden muse" Marie-Therese Walter.
Helena Newman, from Sotheby's, said: "We are delighted that this stunning and monumental portrait, which is part of the defining series that introduced his 'golden muse' to the public eye, fetched such a strong price.
"In recent years in particular we have witnessed the remarkable allure of Picasso's portraits of Marie-Therese to collectors, with La Lecture selling for £25 million - double its pre-sale estimate - in Sotheby's February 2011 sale, and Nature Morte aux Tulipes selling in Sotheby's November 2012 sale for 41.5m US dollars (£26.5m).
"This particular portrait is a striking and notably modern-looking work from one of the artist's most celebrated periods."
The painting sold for £28,601,250.
Also sold at the London auction was the 1914 piece by Egon Schiele, Liebespaar - Selbstdarstellung mit Wally (Lovers - Self Portrait with Wally), which fetched £7.9m.
The sale of the double portrait, in gouache and pencil, broke the record price for a work on paper.