There's a Brough name society that lists the Brough line back through the De Burghs, de Burgo etc (in places like Brewood) and all the way back to Ralph de Limesi, born Rouen c1040. Just put a detail or two into the usual search engines.
BB
It would seem that Thomas Burgh moved from Brewood to the Leek area in the early 16th century (married Maude at Middle Hulme, Leek in 1507). The name change to Brough might have occurred at the beginning of the next century when I have the two children of Richard Burgh (born Windygates, Leek c1570) listed differently as Thomas Burgh (c1590) and Anne Brough (c1601). Anne married John Condliffe. As I've said, there's a lot of material on the Brough family site, and (I seem to remember) on Family Search.