He received a good village education, and was brought up to his father's trade, but moved to Great Yarmouth before he was twenty, where until 1801 he kept a small school in Fighting-cock Row.
He acquired some knowledge of Latin, Greek, and French, was a skilled arithmetician, and wrote a beautifully neat copperplate hand.
Through his love of botany and skill as a collector he became acquainted with Dr John Aikin, Thomas Jenkinson Woodward, Sir James Edward Smith and Dawson Turner.
For nearly twenty years Wigg was collecting material for a history of edible plants, some of which, in manuscript, has subsequently been kept in the botanical department of the British Museum, while a manuscript Flora Cibaria, consisting of extracts from books of travel, has been kept at Kew Gardens.
James Edward Smith acknowledged contributions from him to English Botany (1790–1814), styling him "a most ingenious and accurate observer … eminently skilful in detecting, as well as in preserving, specimens of marine algae".