Here's the first BBC Series on the Parachute Regiment, done in 1982. The parachuting bits are in part 7. As you can tell, the British consider the parachuting the easiest part about being a paratrooper.
Part 1
http://www.youtube.com/watch?v=CmxiVK5I9dU&mode=related&search=
Part 2
http://www.youtube.com/watch?v=ZnhxsjSOJS4&mode=related&search=
Part 3
http://www.youtube.com/watch?v=9vKH5vj9LLU&mode=related&search=
Part 4
http://www.youtube.com/watch?v=BlpDvCY5n2I&mode=related&search=
Part 5
http://www.youtube.com/watch?v=9cekFAimyXM&mode=related&search=
Part 6
http://www.youtube.com/watch?v=O_lRvGb1TNs&mode=related&search=
Part 7
http://www.youtube.com/watch?v=7KqXaZGM_Nc&mode=related&search=