This site shows how common or rare a surname was in 2002. It only covers England, Wales and the Isle of Mann but gives an idea of the feasibility of studying a surname thoroughly.
Springfield turns out to be surprisingly rare - I might look at all that I can find - it may help extend my line back. Stubber(s)field is also rare enough to study in detail, though there are more than I would have expected.
Sawkins is also more common than I would have expected; my Sawkins ancestors were in Kent, but looking at BMD entries from 1837 to 1880 shows they were spread from Salisbury Registration District across to Essex and Kent (especially common in Hampshire) so looking at all the Kentish ones might be feasible.
Great Britain Family Names Profiling (University College London project; the National Trust did provide maps but they now point to this site)
World names maps (also from University College London projects - only covers shaded countries on the maps, not the whole world but non-the-less useful)