The comments above (across the South Atlantic and then east around the African Cape, then return by basically the same route) are correct for convict times. After the opening of Suez affected the tea clippers (which had also gone from China, southwestwards to the African Cape) most were diverted to the wool trade from Australia. I think Cutty Sark had the fastest passage from Lands End to Sydney (~63 days?). She also had the fastest return, in the last head-to-head race with Thermoplylae, which went via the Horn. Sydney - Horn, 23 days; Horn - London, 50 days.

Bligh's troubles compare interestingly with the other famous passages round the Horn, that all went westwards; from Magellan, de Torres & Drake, to Joshua Slocum, the relatively forgotten "first solo circumnavigator". Who also called in at Sydney, rather than Botany Bay.

Cheers, Rowan