He was educated in Chester, and entered the family firm as a clerk and manager at the Bridge Street Mill, Stalybridge.
After acquiring Albion Mills, Platt moved to "Woodlands" on Mottram Road, Stalybridge.
In December 1857 Platt and his wife were honoured by their workforce with a tea party and presentation at Foresters' Hall.
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.
The white marble busts of Mr and Mrs Platt cost £200 and were funded by public subscription from the inhabitants of Stalybridge.