He was educated in Chester, and entered the family firm as a clerk and manager at the Bridge Street Mill, Stalybridge.
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. Platt was well known for philanthropic activities in Stalybridge and Manchester, being a patron of the arts, a supporter of the local Mechanics" Institute and local churches.
His other charitable work included bequests to Chester Cathedral and donations to Owens College.
A portrait of Robert Platt is today in the possession of the University of Manchester
His best known act of philanthropy was the gift of the Stalybridge Public Baths to the town, which opened on 7 May 1870. On 6 February 1871 a pair of sculptures by John Warrington Wood were unveiled at the baths.
The white marble busts of Mr and Mrs Platt cost £200 and were funded by public subscription from the inhabitants of Stalybridge. Accepting them on behalf of the town for placement in the Public Baths given to the town by the Platts, the Mayor stated that they were "beautiful models of the generous donors." Alderman Kirk said that although they were "very good specimens of art" the bust of Mrs Platt was perhaps "not so good a likeness as the other, but taking them together they did very great cr to the sculptor."
Robert Platt acquired a house at "Dean Water" in Woodford, Cheshire.
He was granted arms by the College of Arms.
His arms are described:
BLAZON: Per fesse dancettee Argent and Gules a pale and three frets, one and two, countercharged
Centre for Renewable Energy Systems Technology: A demi wolf Gules, semee of plates, armed and langued Azure holding in the dexter paw a wreath Argent and Gules
MOTTO: Labitur et labetur
Today, the Platts are commemorated by a blue plaque at "Woodlands". and the marble busts are in the possession of the Astley Cheetham Art Gallery.