Born the illegitimate son of General John Burgoyne and the opera singer Susan Caulfield, Burgoyne was brought up by the 12th Earl of Derby (a nephew of his father's late wife) following his father's early death. Educated at Eton College and the Royal Military Academy, Woolwich, he was commissioned as a second lieutenant in the Royal Engineers on 29 August 1798. Promoted to lieutenant on 1 July 1800, he took part in the Siege of Malta in Autumn 1800 during the French Revolutionary Wars before becoming aide-de-camp to General Henry Fox. Promoted again, this time to second captain on 18 March 1805, he took part in the capture of Alexandria in February 1807 and the subsequent occupation of Rosetta in April 1807.