24 June 1815 Appointed Hospital Assistant.
1 Aug 1817 Conferred the degree of Doctor in Medicine (MD) by the Senatus Academicus of the University of Edinburgh after having gone through the appointed examination, and publicly defended his inaugural dissertation on De Ophthalmia.
12 Apr 1821 Assistant Surgeon 38th (1st Staffordshire) Regiment of Foot.
18 July 1821 Assistant Surgeon 72nd (Highland) Regiment of Foot, by exchange.
29 Dec 1826 Appointed a Staff Assistant Surgeon vice Nelson placed on half-pay. The vacancy created in 72nd Foot was filled by Hospital Assistant Samuel John Stratford on 18 Jan 1827.
1827 Married Helen Dixon aged 24 years, born at Morpeth, Northumberland.
17 May 1831 Appointed Assistant Surgeon 94th Regiment of Foot vice Assistant Surgeon Edward Josias Bulteel who exchanged to staff as Assistant Surgeon to the Forces vice Burrell.
Malta 1832 Arrived from Gibraltar with his regiment.
Malta 1833 On regimental duty.
Malta Jan–Feb 1834 On regimental duty. His accommodation consisted of two rooms in the General Hospital.
Malta 8 Mar 1834 Staff Assistant Surgeon. Exchanged from 94th Foot with Assistant Surgeon Maginn Daniel Wedgworth.
Malta 7 Apr 1835 Embarked for England on sick leave.
5 May 1837 Aged 42 years. Promoted surgeon after 22 years service. Had served between 20 and 21 years on full pay before gaining promotion.
Malta Dec 1837 Arrived at Malta as Surgeon 77th Foot.
Malta 1838 At Malta as Surgeon 77th Foot.
Malta 1839 Surgeon 77th Foot.
Malta 27 Apr–27 Oct 1840 On leave.
Malta 1841 Surgeon 77th Foot.
Malta 5 Feb 1842 Left for Corfu.
16 Dec 1845 Staff Surgeon 1st Class.
Malta 20 Mar 1851 Arrived at Malta.
Malta 1852 Staff Surgeon 1st Class.
Malta 1853 Staff Surgeon 1st Class.
Resident at 3 Strada Mercanti Valletta.
Malta 24 Mar 1854 Appointed PMO of the Expeditionary Force to the Crimea by the Director General AMD Andrew Smith, with the rank of Deputy Inspector General.
25 Apr 1854 Burrell left for Turkey on the steamer Emeu. He arrived at Scutari on 30 April and in May took charge of the Military Hospital at Scutari. His appointment, however, had been cancelled, as the augmentation of the Force to four Divisions required a more senior officer of Inspector General rank. Inspector General Hall John, PMO of the Bombay Presidency, was chosen to head the medical department. Hall arrived at Constantinople from India on 17 June 1854. As a result, Burrell resigned his commission and returned to England. Burrell was placed on half-pay on 24 June 1854.
14 Oct 1857 Placed on half-pay with rank of Deputy Inspector General, so as to be specially employed on the Barrack and Hospital Committee.
Author: Report on the plague of Malta of 1813 presented to both Houses of Parliament by command of Her Majesty. General Board of Health Appendix V to second report on quarantine. London 1854. Burrell maintained the plague to be due to a peculiar atmospheric constitution as an initial cause, which then developed assisted by season and local conditions. The transmissibility of the plague from person to person out of the noxious atmosphere in which it originated had not been proven. Quarantine restrictions utterly failed to arrest the progress of the plague. On the contrary, observed Burrell, where these restrictions were carried out to their utmost limits by an absolute power there the disease persisted longest and the mortality was greatest.