Sir George was born in London in 1772 and was a renowned British naval officer, eventually becoming Admiral of the Fleet and First Sea Lord.

The original District was bounded on the north by the Swan River from Fremantle to the mouth of the Canning River; on the east by a line from Bull Creek to the junction of what is now the intersection of the Albany and South Western Highways in Armadale; on the south by a line from Armadale to, and including the Rockingham townsite; and to the west by the Indian Ocean.

On 21 January 1955, it was renamed Cockburn,[6] after a successful referendum underlined the desire for recognition of the District's independence from Fremantle.

However, the council has "no involvement in or responsibility for any functions relating to the control and management of the islands", which are administered directly by state government agencies.

The suburbs of the City of Cockburn with population and size figures based on the most recent Australian census:[14][15] As of 2024[update], 140 places are heritage-listed in the City of Cockburn,[41] of which 21 are on the State Register of Heritage Places, among them the Coogee Hotel the Newmarket Hotel and the Woodman Light.