Thomas Iddo Jenkinson also played in the football league for Sheffield United & Grimsby Town in his younger days - https://en.wikipedia.org/wiki/Thomas_Jenkinson_(footballer,_born_1877)
Thank you so much for pointing me towards Thomas Iddo Jenkinson's footballing history.
I have found many newspaper mentions of him regarding his Grimsby Town career - he was a very talented player, it seems, from the reporting - and this has now led me to discover a photo of him on a wonderful site which sets out to record the photographs of all the management and players of the team over its whole history.
Fascinating! I have urged my daughter to talk to some of her older neighbours who may still recall Thomas's son, Frank (the schoolteacher) who died in 1970 and his wife Alice who died in 1999, both at Marlcliffe Road.