It is an example of adding emphasis, and being "extra polite", as Josh61 says in his answer, but I think there's some extra subtleties which are worth pointing out.
When we interview someone in front of an audience, and reach the end, we (the interviewer) need to emphatically signal to our interviewee and the audience that the interview has ended: this is the interviewee's cue to relax and the audience's cue to applaud or whatever. Simply saying "Thank you" is not a strong enough cue for this purpose: it needs to be something that catches everyone's attention, and something that you would not normally say during the interview.
Combined with a particular rise-and-fall speaking pitch, ("med med hi-hi-hi low low") "Thank you very much indeed." works very effectively: the "indeed" acts like a very clear sign saying "The End".
In this sense, the phrase "Thank you very much indeed" is actually operating on several levels at once: it's an English sentence but it's also an aural cue operating on a level beyond language - almost like music. Even someone who didn't speak english could learn to recognise it as a "This is the end" cue, and it will tend to alert even the people in the audience who aren't paying good attention.
Even if there's no live audience, an interviewer may still adopt this technique, partly out of habit but also to tell the viewer at home and the interviewee that they've reached the end.