Henry Cornish (died 1685) was a London alderman, executed in the reign of James II of England.
He was a well-to-do merchant of London, and alderman of the ward of St. Michael Bassishaw; in the London Directory for 1677 he is described as a factor residing in 'Cateaton Street, near Blackwelhall Gate.' He was a presbyterian in religion, and in politics was a strong whig. On 24 June 1680 he was chosen sheriff of London in conjunction with Slingsby Bethel.
More information on the Wikipedia page [1], and mention here.