Burrows commenced duties at the South Australian Museum on 18 March 1944 in the capacity of Museum Attendant. Between 1946 and 1950 he assisted the Ethnologist, NB Tindale (see AA 338), with the re-organisation and renovation of the 'Melanesian Hall' or the Pacific Cultures Gallery. After taking night classes in drawing and design Burrows was appointed as Museum Assistant to Tindale in July 1949. His duties included the general storage and care of all ethnological material, the handling and registering of newly acquired specimens, together with the preparation of detailed lists and catalogue cards. His work in the preparation and display of ethnological specimens in the public galleries included the Indonesian Hall, and Burrows also assisted in the reorganisation of the reptile gallery. In 1958/59 Burrows' title changed from Assistant in Anthropology to Assistant Preparator, and in 1964/65 to Preparator. Retired in April 1968, Burrows was reappointed as a temporary Museum Assistant in Anthropology on annual review; a position he held from July 1968 to June 1971.

Burrows was greatly interested in anthropology, and during annual leave he and HM Cooper (see AA 64) visited and researched Aboriginal rock engravings located in the Orroroo district of South Australia. This work lead to a publication: HE Burrows, 'Rock Engravings from the Orroroo District, South Australia', Records of the South Australian Museum, 15 (3), 1967, pp. 363-369.

Related collection: AA 64 Cooper.