The only properties Edward VIII sold were Balmoral and Sandringham, both of which belonged to him under his father's will as the eldest son and successor to the throne. He did not receive any additional bequests from George V because as The Duke of Cornwall, he had received its income for years as the heir, while his brothers did not. The properties were valued at 300,000 sterling, but this lump-sum was not paid directly to The Duke, rather an equivalent amount was used to purchase War Loan bonds to generate 11,000 pounds annually in tax-free income. His brother supplemented this income with an allowance of 10,000 sterling per year.
Keep in mind The Duke had lied about his personal means when George VI initially agreed to a 25,000 sterling annual income, stating he only had 5,000 per year, when his fortune was worth over 1 million sterling from years of income from the Duchy of Cornwall. This does not include substantial sums of money he spent from his brief time as King from the Duchy of Lancaster, most of which was used to purchase jewels for Wallis.
The Dukes of York, Gloucester and Kent each received about 1 million sterling in trust (about $30 million today) from their father's estate, believed to be limited to the income only, with the grandchildren inheriting the principal. Unfortunately, due to World War II, currency controls and inflation, much of this money was greatly diminished by the early 50's.
The Crown Estate is inalienable from the State, although it technically belongs to the Crown in the person of the Sovereign. If the monarchy was abolished, those assets would remain with the Exchequer.
