The "Classic Briar" character is the same guy as Constable Briar from the first game, while the new "PC Rob Briar" character is his son.
Mr. Foster is descended from people who lived on the Anglo-Scottish Border.
In The Steel Bonnets, Foster is listed as one alternate spelling for Forster, a common surname in the Border area. Border folk have spread themselves far and wide since the age of the reivers, and Mr. Foster could be a descendant. If this were the case, it certainly wouldn't make him the first Borderer-descent person of a literary inclination who worked in a financial institution in the Square Mile...