The last-known portrait of the painter had been expected to sell for between two and three million pounds (2.2-3.3 million euros, 3.2-4.8 million dollars) at Wednesday's auction, Sotheby's said.
"This is the most important 17th century British portrait to come on the market in the last two decades. It was an opportunity we could not miss," said the buyer, art dealer Philip Mould.
The previous price paid for a Van Dyck was three million pounds.
The 1508 drawing by Raphael was a record price for any work on paper sold at auction. "Head of a Muse" has only been seen once in public in the last 50 years and had not been put up for general auction for more than 150 years.
The painting by Rembrandt, held in private for the last 40 years, called "Portrait of a man, half-length, with his arms akimbo" was a record price for the artist at auction.
A Domenichino painting sold for 9.2 million pounds on Tuesday, also a record price for a work by the artist at auction.
Source: AFP European Edition