The white leather flat shoes are thought to have been worn by the late princess when she was 19 years old, during the time she worked as a nursery assistant.
The shoes were left by Diana at the house of an anonymous friend in about 1977-78.
There are photographs of her wearing similar shoes while working as a kindergarten teacher aged about 19, Dominic Winters Auction house said.
A note from the princess, discussing meditation and French philosophy, written on Kensington Palace notepaper sold for 1,400 pounds at the auction, 'BBC News' reported.
Three other letters written by the prince fetched between 230 pounds and 320 pounds.