The bookies runner calling himself an Accountant is stretching things a bit but a Turf Accountant is a bookmaker licensed to take bets on horse races.
Like poster youngtug , i have a relative who was definately a bookies runner (a grt grandads brother in Birmingham) and he described himself as an "accountant" too
. Have also seen more than one criminal record were the convict has the occupation "clerk" . Two distant "cousins" on completey different branches are described as "clerks" in criminal records . One is covered in tattoos and the other one has scars that are probably from knife fights (thumb , ear ect) . There are also mugshots of them looking nothing like "clerks" at all !!!

(this was in Australian mugshots after they had emmigrated from England late 1800s)