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Little is known of Simpson. He seems to have been a quiet, hardworking seaman, serving as Quartermaster's Mate, with no mention of disciplinary problems. He took no part in the mutiny, and during the voyage of the Launch, he sided with Fryer in his disputes with Bligh.

He apparently was not available to testify at Heywood's trial, and it was his and Tinkler's absence that formed an important part of Heywood's plea for clemency.

He was found dead in his hammock on the 'Princess of Orange' in 1801. No cause of death was given, and his personal effects were turned over to his father in the Lake District. (Caroline Alexander, "The Bounty")