Margaret's son Viscount David Linley, 44, was 'absolutely thrilled.'
He expected 'two to three million' pounds (A$5 million to A$7.5 million) from the two-day sale at Christie's auction house, said Dermot Chichester, chairman of Christie's UK.
The final total was 'absolutely astonishing,' Mr Chichester said following the sale of many sentimental possessions of Queen Elizabeth II's only sibling, including her wedding tiara.
"It's an historic sale and a historic result... This is about collecting and about passion, and about royal enthusiasts wanting to buy an item from the collection," Mr Chichester said.
A total of 4,061,048 pounds (A$10 million) was raised on Wednesday, compared to 9,597,680 pounds (A$24 million) on Tuesday, Christie's said.
A romantic portrait of the princess, who died in 2002 at the age of 72, sold on Wednesday for 680,000 pounds (A$1.7 million), the highest price paid at auction for a work by the painter Pietro Annigoni.
The 1957 portrait of Margaret shows her wearing a diaphanous dress and wrapped in a cloak reminiscent of the religious frescos the artist painted as a younger man.
Earlier Wednesday the princess's nine-carat solid gold Cartier cigarette case with a sapphire clasp sold for 102,000 pounds (A$255,000).
It was a Christmas present to Margaret from her father in 1949, three years before he died and is engraved with the inscription: "From her very devoted Papa."
Gift clocks more than $3 million
Highlights from Tuesday's auction included a Faberge clock, a gift from Margaret's grandmother Queen Mary, which sold for 1,240,000 pounds (A$3.1 million).
The tiara she wore for her 1960 wedding to Lord Anthony Snowdon sold on Tuesday for 926,400 pounds (A$2.3 million).
Viscount Linley and his sister Lady Sarah Chatto, 42, hope to pay inheritance taxes with proceeds from the sale, but also give some to charity.
The collection included pieces that were inherited, presented as gifts or personally acquired by the princess and reflected her celebrated style and elegance.
The sale has attracted some controversy amid claims that Margaret's ex-husband Lord Snowdon was unhappy that some of the items were being auctioned.
Lord Snowdon, who was married to the Princess between 1960 and 1978, wrote to Christie's questioning whether his children had the right to sell them.
However the auction house said there was no question of any of the pieces being withdrawn from the sale.
Margaret, the younger sister of Queen Elizabeth II, was known for her glamour and sense of style. She died of a stroke at the age of 71 in February 2002.