He was born at High Close Hall near Plumbland, the son of local gentry, George Brownrigg. William's mother, Mary Brownrigg, was from Ireland.
William was educated in Latin and Greek by a local clergyman from the age of 13 and by the age of 15 was an apprentice to an apothecary in Carlisle. Then followed two years studying under a surgeon in London before going to Leiden where he studied under Boerhaave, 's Gravesande, van Royen and Albinus. He graduated in 1737 with his thesis "De Praxi Medica Ineunda" – about the environment where the clinician practises medicine. He gained the degree of Doctor of Medicine (MD).