The son of Alfred Edward Stamp, Stamp was educated at Gresham's School, Holt, and the Inns of Court. A barrister, he became a High Court judge of the Chancery Division and in 1971 a Lord Justice of Appeal. He was appointed a privy counsellor on 5 April 1971.
He should not be confused with antecedents of the same name, Mr Edward Blanshard Stamp (1805 – 1847), of Brighton, and Mr Edward Blanshard Stamp (d. 1908), of Hampstead.