Burr took office at London on 29 June 1839, sailing with his family aboard the barque Cleveland on 24 July, but did not reach Port Adelaide until 18 December 1839 to begin active duty.
Burr was then detailed by Gawler to accompany the experienced John Hill in the cutter Water Witch to Northern Yorke Peninsula.
The pair then carried out further exploration on their homeward journey to Adelaide, being the first Europeans to traverse this region, discovering extensive fertile land.
In April 1842 Burr accompanied Governor George Grey on a 14-day examination of the country around Wellington, Lake Albert and the Coorong, again preparing charts.
The Burr family's original residence was at Meadows, but they subsequently established Grove Cottage on fifty acres of fertile land beside First Creek at what is today's Adelaide scenic suburb of Hazelwood Park.
Burr was returning to Adelaide from this ineffectual search when, taking one of the men with him, he decided to leave the coast to cross eastward over the rugged Southern Flinders Ranges.
In 1840 Eyre had sighted and named the distant and towering Mount Remarkable from near Crystal Brook, but did not venture in that direction, remaining on the western (coastal) side of the Flinders Ranges, and so missed what Burr discovered.
Crossing to the eastern side of the ranges, Burr found that they overlooked extensive 'well-wooded and watered country', now called the Willochra Plain, stretching from Melrose northward toward Quorn, east toward Orroroo, and south toward Laura.
When in August 1844 Charles Sturt assembled his Central Australian Expedition he endeavoured to obtain Burr's services as draughtsman.
[12] In August 1847 Burr was persuaded to resign from government service to accept the office of General Superintendent of the Burra copper mine, being also immediately appointed a local magistrate.
Burr's dismissal in September 1848 resulted in his launching successful civil litigation against the directors, gaining substantial damages.
[17] The Grove Cottage estate, located on modern-day Greenhill Road, was purchased by the Clark family who renamed it Hazelwood Park.
Nearly uniquely among government officials, he was present during the whole of the riots, boldly attending all the mass meetings of diggers in November 1854, at one of which there was a threat he could be shot as a spy.
[18][19] Following the Eureka riots Burr continued to undertake survey work at Ballarat and other goldfields, while remarrying at Castlemaine in 1857 to widow Isabella Gillis, nee Rough.
[21] Burr died suddenly of a heart attack on 25 September 1866 in Flagstaff Gardens Reserve, West Melbourne, Victoria.
Despite his ignominious end, for many years Burr was an influential contributor to expanding the geographical and geological knowledge of the emerging colony of South Australia.