Why do BBC shows have 'Producers'??

[old_tv_nut]

Well, at least we have established that the discussion is about people with financial responsibility. In U.S. radio and TV, "Producer" is also used to denote a staff position that chases down source material, gets copyright clearances, wrangles guests, etc. etc., in other words makes sure the essential and auxiliary elements of the program are obtained and available. [Edit: I believe these producers often do not appear in the credits.]