Final answer:
Captain James Cook's exploration of the eastern coast of Australia in 1770 led to the English claim on the continent and eventually to the use of the land as a penal colony.
Step-by-step explanation:
The exploration that formed the basis for the English claim on Australia was that of Captain James Cook. In 1770, Captain Cook, serving the British navy, sailed aboard the Endeavour and reached the eastern coastline of Australia. He landed at Botany Bay, near present-day Sydney, and claimed the region for Britain, naming it New South Wales. This event was pivotal as it marked the beginning of English attention towards the continent, especially as a potential solution to ease the overcrowding in British prisons after the loss of the American colonies.