A student of mine studies vocabulary from the Vanessa Feltz show on BBC Radio London. This is good if you are an advanced student.
For intermediate and advanced students, many programmes on BBC World Service are suitable.
Radio shows can be a more effective way to learn intensely than TV shows.
Here are a few shows that I suggest to my students. The first 4 are talk/panel shows:
1. Would I Lie to You
2. Room 101
3. Graham Norton show
4. Good Morning Britain
5. First Dates
6. Dragon's Den (Business)
7. The Apprentice (Business)
There are many clips available on Youtube. I hope this helps!