If unsuccessful, he was to backtrack to the Falklands and claim them. In either location, he was ‘to make purchases, with the consent of [the] Inhabitants, and take possession of Convenient Situations', locate suitable harbours, and then proceed into the Pacific for the second set of objectives.
Those, according to his instructions, involved Terra Australis Incognita and the search for a route to Hudson’s Bay in through the long-sought Northwest Passage. If found, he could return home that way, but if that quest was unsuccessful, or provisions were short, he could cross the Pacific and return via the Indies.
Byron, whose inclination seemed to be to take the shortest route that his instructions permitted, started by ruling out the suggested approach to Pepys Island via the Cape of Good Hope, and headed instead for Port Desire (Puerto Deseado) in Patagonia. He arrived there on 18 November 1764 and noted the presence of remarkably tall natives, to whom ‘The Stoutest of our Grenadiers would appear nothing’ in his journal. That would bring him a degree of grief when John Hawkesworth's somewhat romanticised version of the journal appeared in print in 1773.
From Port Desire Byron headed out into the south Atlantic and reached Cowley's co-ordinates for Pepys Island in January 1765, but there was no sign of the island. When it became clear that the search for the non-existent island was pointless Byron headed for the Falklands, anchored at a place he named Port Egmont and formally claimed the islands for George III.
Although he made a cursory inspection of north coasts of West and East Falkland, Byron, who seems to have been disinclined to hang around, failed to notice Port Louis, the French settlement Louis de Bougainville had recently established on East Falkland's Berkeley Sound. He did, however, need to rendezvous with the storeship HMS Florida at Port Desire, to replenish supplies before venturing into the Pacific.