Hi Tommy, Not sure where you are in South Yorks.
I know of one spot on the Don in Sheffield, quite a nice steady stretch with a little more depth than average. From memory it is just above the Stevenson road bridge. The river is a few feet below the bank and railed off. However sections of the railings can be opened to give fishing access. I have seen wheelchair anglers there in the past, I don't know any contacts to obtain keys though. There may be notices up at the site.
Secondly, it is also possible to access the river further into Sheffield centre from Warren Street. There is an entrance marked 'Five Weirs Walk' take this and turn right at the river, there is a large wooden platform above the weir with low railings. Before they dug the weir out this was an excellent spot for chub, perch, grayling, dace and the odd trout. This is 'free'.
Hope this helps.
The Sogster