On the Christening records of his daughter, Elizabeth it shows the family address as Ordsall Lane (which is in Salford, Manchester) and Roberts occupation as Dyer.
Investigating I have found an entry in The National Archives which shows an old map of the area of Ordsall Lane and a large factory called Ordsall Dye Works. (Link below)
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NNTL-47L : 9 March 2018, Robert Hawthorn in entry for Robert Hawthorn, ); citing St. Bartholomew, Salford, Lancashire, England, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,786,460.
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JSBR-53D : 11 February 2018, Robert Hawthorn in entry for Mary Hawthorn, 01 Sep 1872); citing St Bartholomew, Salford, Lancashire, England, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,786,460.
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