[Chip Chester]

There are various different types of producers in TV and film. Some have the original idea, and wrangle the money -- either finding it or supplying it.
The others wrangle the production process, overseeing budget, staffing, production and post processes with an eye toward realizing the creative vision.
It's a balance between the director and producer, but ultimately the producer has responsibility for control of the project. This all needs to happen in a corporate setting like BBC. If a BBC producer goes ten million over budget, he can certainly be canned -- or made "no longer a producer".

I'm guessing that the BBC also supports externally-funded business model (here's a show, we'll make it, you buy it and air it) sort of like most US TV.

Wiki probably has good descriptions, that I'll let you discover. Look at Producer, Executive Producer, Line Producer, etc.

Contributing writers, actors with decision making privileges or a significant financial stake, creative mentors who are "on call" (like Jon Stewart for Colbert's old and new show), and folks who did something for the production, but are not otherwise classified are given producer, co-producer, or assistant producer credits.

Chip