Just managed to register with the forum.
I am the owner of the painting, and I am very grateful to ceegee for starting this thread and to everyone who has replied with ideas and suggestions.
It seems that there were two Robert Hudsons, father and son, who were both painters.
Robert Sr was known as a painter of "fresh out-door subjects, such as birds nests and apple blossoms". This, I believe, is an example of Robert Sr's work:
Robert Jr lived from 1852 to 1884, dying at the age of just 32. Thanks to the Royal Academy in London and Graves Gallery in Sheffield, I have some additional information.
Robert Hudson Jr showed a painting at the Royal Academy in 1877, titled “Companions in Age”
His address at the time was given as 441 Glossop Rd, Sheffield.
According to the Dictionary of British Artists 1880-1940, Hudson Jr also showed at least 2 paintings at the Royal Scottish Academy.
To be included in the Dictionary of British Artists 1880-1940 one of the major auction galleries had to have sold a painting by Robert Hudson Jr for at least £100 between 1970 and 1975.
Graves Gallery in Sheffield
Robert Hudson Junior
Born 1852, Sheffield, Yorkshire, son of Robert Hudson Senior, Artist, Furniture broker
1861 Census: aged 9, Scholar, living at 100 Devonshire Street, Sheffield, Yorks, with parents, 4 siblings, 1 servant (RG9/3478. folio 72)
1871 Census: aged 19, artist in oil colours, living at 64 William Street, Sheffield, Yorks, with parents, 4 siblings (RG10/4670, folio 67. p21)
Studied Sheffield School of Art
Travelled in Switzerland, Scotland and North Wales
1877: Marriage reg. J1877 to Mary Holiday, Ecclesall Bierlow, Sheffield, Yorks.
1877: Exhibited Royal Academy, London
Exhibited with Royal Society of British Artists, London
Founder (?) Member of and exhibitor with Sheffield Society of Artists
Patronage of John Newton Mappin, Rotherham brewer.
1881 Census: aged 29, artist, landscape painter, living at 8 Havelock Street, Sheffield, Yorks, with wife (RG11/4633. folio 45. p32)
Died 6 April 1884, aged 32, Ecclesall Bierlow, Sheffield, Yorks.
Obituary, Sheffield Daily Telegraph, 7 April 1884
Image below from http://ceegee-viewfromahill.blogspot.co.uk/2017/02/robert-hudson-sheffield-artist-1852-1884.html
Museums Sheffield holds a paining by Robert Jr that was painted in Endcliffe Woods.
I contacted the parks department for the Endcliffe area and was given this suggestion: "Porter Valley had a number of working buildings around all the Dams including Dams that are no longer around."
Here are some additional photos (deliberately over exposed and lightened) of the front, back, and details of the painting.
Additional images of paintings by Robert Jr at https://artuk.org/discover/artists/hudson-robert-18521884.
Given that Robert Hudson Jr is known to have painted scenes in Switzerland, Scotland, and North Wales as well as in the Sheffield area, it may be that the painting I have was not painted in Sheffield at all.
At the moment, I am following up the Royal Scottish Academy, Royal Society of British Artists, and Sheffield Society of Artists.
I have never visited Sheffield, but looking at some of the suggested locations on Google Maps, it is clear that the area has changed a great deal in the intervening years and that the chances of the location in the painting being identified (if in or around Sheffield at all) are small.
Come what may, it seems that Robert Hudson Jr was a highly accomplished artist who died way too young and was forgotten far too easily for a man of such evident talent.
With thanks for any ideas or suggestions.