They do have some really good ones.
It is interesting that in different episodes they often switch the dominant/passive roles, so it's not fixed as in Laurel and Hardy.
Video 1. Are we the Baddies? by Mitchell and Webb. Source. See also:
Video 2. Discoverer by Mitchell and Webb. Source. Makes fun of the many terrible naming choices British navigators have made while discovering/rediscovering new lands.
Video 3. Homeopathic A&E by Mitchell and Webb. Source.
Video 1. The Day Today Episode 1: Main News Attack. Source.
Video 2. WAR! by The Day Today. Source.
Video 1. Anti-Piracy Ad by The IT Crowd (2007) Source.