I looked at some electoral registers in the Local Studies Library:
Robert and Priscilla JONES are at 3ct,1 Burns Road in the roll for 1935/6.
In the volume for 1936/7 the voters listed are William Henry and Eva COATES.
So they must have left Burns Road between those dates..
I tried looking for the later address but I was confused by the fact, which I now see, that you have given two different street names 'St Mary Road' which I automatically assumed was St Mary's Road; and then Queen Mary Road, which I'm guessing is the right one.
In 1951 there was a Robert Jones at 471 Hastilar Road South which I think must be in the same area as Queen Mary Road.
edit: I meant to add that there were no electoral rolls in Sheffield after 1939/40 until May 1945.