Does the Duke of Westminster own Buckingham Palace?

Buckingham Palace is owned by the "Queen in right of the Crown". Meaning that she doesn't own it as a private person but rather as the personification of the crown. As long as the monarchy remains, the palace will be owned by the sovereign, but he or she doesn't have the right to sell it. The Duke of Westminster owns a lot of land in London but Buckingham Palace is not one of them. Technically the Queen owns more of London than any one, through the Crown Estates, Royal Parks, Royal Palaces and the Duchy of Lancaster, but once again she doesn't have the right to sell any of these as a private individual.