DerekT on Family Tree Circles

I never knew my paternal grandfather, and until late in life I never had the time or inclination to research family history. As the family scattered (from England) throughout the world we all lost touch. I ended up in S.Africa. I am therefore not able to visit any UK archives.
Between the 1861 and 1881 censuses of Leeds, Yorkshire the surname was changed from Taylor to Taylor Tunnington, (no hyphen).
The Commercial genealogy firms cannot give me an answer, although they offer to "search" for a sizeable fee! As I am on a modest pension I cannot justify unnessary expenditure on a search.
Does anyone have suggestion on this problem?
Incidentally we though that Tunnington was uncommon, but I have been surprised at the large number of people with that family name, (none connected).
DerekT.