I've checked out the 1837 Rotherham area in White's Gazetteer, and only two Glass manufacturers are listed: Close & Clark at Catcliffe, and Beatsons in Rotherham. Beatsons would be a 5 mile journey each way to and from work, and Catcliffe is even further, so I doubt that either fit the bill. There were Glass Manufacturers in or near Mexborough some years later as I noted above, but none are evident in 1840.
To explain my interest, a certain William Thynn Gillinder is the glass worker who was living in Mexborough in 1841, with his elder brother Thomas (also a glass blower) and his family. They must both have worked somewhere!