We should also remember On The Hour, the original radio precursor to The Day Today, though I think the TV series is more important.
My own favourite Chris Morris production is probably his Radio 1 series with the painfully embarrassing improvised tasks he'd set his hapless roving man on the scene.
I think that was also the one that got him temporarily banned from the Beeb for implying - but not outright stating - that Michael Heseltine (very senior British politician at the time) had died from a heart attack.
Edit: Ah, here. Typically facetious interview with "close personal friend, colleague and bass player of the Jam, Bruce Foxton"
"hit the ground screaming",
"which of your bass lines would be a suitable sort of lament", etc, etc