There are a couple of websites that you might enjoy looking at to find out about Barton Road.
This one has digitised copies of street directories, including several of Exeter. http://www.historicaldirectories.org/hd/index.asp
The 1916 Besley's Directory of Exeter and Suburbs shows Barton Road with quite a few gaps in the numbering so I guess that this was when it was partly built. Even then the numbers go from 56 to 117 and follow up one side and back the other as they do now. Worth looking at an earlier and later directory to see what happens to the house numbers.
You should be able to see who lived in your own house too.
The other site gives maps http://www.old-maps.co.uk/index.html
If you put these coordinates into the boxes on the left of the screen, it will take you staright to Barton Road (290982 91530)
Then choose the 1:2,500 maps from the list on the right and once they've loaded, zoom in for extra detail. This is a great site for seeing the development of an area over the years.
I have the 1965 Kelly's for Exeter - if you want to know who was living in your house at that date let me know.