If not there then where?
As any fule kno, there are numerous different historical origins for surnames, and Cosby (I would suggest) is of the toponymic variety – derived from a placename. And the only place in England called Cosby down at least the last thousand years or more is Cosby in Leicestershire. You can check gazetteers till you're blue in the face but I don't think you'll find another,
So, therefore, all families called Cosby are overwhelmingly likely to originate from the village of Cosby in Leicestershire, identified as Cossebie in the Domesday Book of 1087. And their patriarch, plus or minus a generation, is therefore Cossebie 1, as designated in the online Domesday Book, known to his contemporaries as Cossa of Cosby, or Robert of Cosby, if the Rude Forefathers tabulation is taken on trust.
OrnaVerum has so far [Apr 2016] identified at least three different variations on the Cosby theme – the Midland / Stradbally one, the London / West Country one and the London / French one.
Had there been three different placenames Cosby, then each these Cosbe cohorts could have distinct topographical origins. But there weren't, so they didn't.
I've so far failed to find exactly at what point or points the various branches diverged, but feel confident that some brighter spark than myself will sort it all out. Meanwhile, I'd like to greet Cossebie 1 in his native tongue: