I might be able to help you here, Dorothy. I don't know if you are familiar with the area but Sawmill Row wasn't in Bedlington town but in the greater area of Bedlingtonshire. It was situated by the sawmill that once stood in Guidepost, roughly to the east of the junction between Sheepwash bank and Stakeford lane. The sawmill, but not Sawmill Row, appears on this OS map from 1866. Note that there are no houses in front of it facing Stakeford Lane and only one row of houses running north to south directly to the west of it:
Census enumerators had strict routes to follow so in the 1901 census we can see that Sawmill Row is situated between the community of Guidepost (no street names given) and Ford Terrace - which is followed by Freehold Terrace. Freehold Terrace appears to be the elder of the two as it appears on early maps but is not named. However, the 1922 OS maps show both Terraces with name so they must have been built between 1866 and 1901. (Ford terrace to the south of Stakeford lane, then called simply 'High Street'):
and Freehold Terrace to the North of High Street:
Note on the first of those two maps that a new street has also appeared running at right angles to High Street and parallel to Blyth Terrace. I believe this is Sawmill Row but it is also possible that the street named Blyth Terrace was previously Sawmill Row as it stood on its own next to the sawmill. Unfortunately I can't find the name on any maps.
Eggy, your a genius with maps. Can you do some sort of collage with arrows and pretty bits that show this as a then and now kind of picture?