eStream allows us to record programmes covered by the ERA licence off-air and also gives us access to a large archive of BBC and other programmes. Once these programmes have been added to eStream you can add them to your Moodle page just like any other video (or audio). What's more you can use the 'chapter' functionality to isolate a particular clip from a programme and add that to your course.
To request a current programme to be recorded or to see if an old programme is available in the archive, contact the library using firstname.lastname@example.org
Many more guides to non-Moodle specific aspects of eStream are available on the Planet eStream Training resources page.