Hello Jill
New Street still exists off Doncaster Road oposite the Miners Arms, some houses were demolished just before 1939 and the rest after the war.
I thought Alfred place was in what was known as the Brickyard again mainly demolished 1936-9 the people were rehoused in Windhill council housing estate. My brother says he thinks Alfred place was in between Herbert Street and Doncaster Road, stone houses demolished 1950 ish.
Doncaster archives and Doncaster Family History Society have Electoral Rolls for the period you are researching.
The archives also have early maps of Mexborough but these only name the main roads.
As to which Coal Pit, people in my street worked mainly at Denaby Pit but some worked at Cadeby some at Barnburgh, my uncle Harry worked at Kilnhurst Pit. It depended who was setting on and who was laying off workers.
The miners pre war were up at 5 AM, walked in there clogs and pit clothes to the pit and were often sent home not needed, no pit baths, no toilets, no canteen, pay for your own pick and shovel and to have your pick sharpened. The good old days???.
Luckily for us my father did not work in the mines and would not allow his children to.
Adwick le Street - the nearest coal mine was Brodsworth, one of the good mine owners, I think from Notts who built a model village, very good houses for his workers about 1904 ish???
Regards Oly a Mexbro-ite