The South Island was an island of New Zealand.
History
In 1770, the Endeavour sailed along the coast of the island with the First Doctor and Ian Chesterton on board. The crew attempted to stop on several occasions, but failed to do so, due to the lack of hospitable bays on their route. (AUDIO: The Transit of Venus)
During the Cybermen invasion in December 1986, the crew of the Zeus IV mentioned that they were over the South Island of New Zealand. (TV: The Tenth Planet)