Burrell was born in Longhoughton, Northumberland, England, on 26 February 1777. He was the second son of John Burrell, esq. of Longhoughton, and his wife Barbara Peareth of Newcastle. He joined the British Army as an ensign in the 15th (East Riding Yorkshire) Regiment in 1797 and was promoted to lieutenant later that year. In 1805, he joined a company and when on passage to the West Indies, the transport ship in which he was embarked was attacked by a large French privateer schooner, which was beat off with great loss. Burrell became a major in the 90th Light Infantry in 1807, was at the capture of Guadeloupe in 1810, and served during the war in Canada in 1814 and 1815, having commanded the post of Fort-Major during the winter of that year. He proceeded to Europe in 1815, but arrived too late for the Battle of Waterloo. Having marched to Paris, he remained there until the occupying army was formed in December before returning to England in July 1816.