Robert Platt was born in Stalybridge, Cheshire, the son of cotton manufacturer George Platt and his wife Sarah. He was educated in Chester, and entered the family firm as a clerk and manager at the Bridge Street Mill, Stalybridge. On the death of his father in 1831 he assumed sole control of the business. In 1839 he married Margaret Higgins of Salford, daughter of William Higgins. in 1839. He expanded his business by the extension of the Bridge Street Mills and the construction of Quarry Street Mills. After acquiring Albion Mills, Platt moved to "Woodlands" on Mottram Road, Stalybridge.