Dreamless Sleep and Sweet Disaster

Dreamles Sleep is a 1986 short by David Anderson on the subject of nuclear disaster; according to Animate Online it won the Hiroshima Peace Prize.

It was made as part of Sweet Disaster, a Channel 4 series consisting of animated visions of the apocalypse; other Sweet Disaster shorts I know of are Aardman's Babylon, directed by Peter Lord and David Sproxton (the easiest to get ahold of as it is included on the Aardman Classics DVD); Paradise Regained and Conversations by a Californian Swimming Pool, directed by Andrew Franks; and Death of a Speechwriter, directed by David Hopkins. In addition, Hopkins scripted each of these films aside from the dialogue-free Dreamless Sleep.

Babylon, Aardman's contribution to Sweet Disaster.

Presumably Conversations by a Californian Swimming Pool.

Lesley Keen's Burrellesque

Burrellesque is a short film from 1990 by Scottish animator Lesley Keen. The opening titles explain the film's origin:

In a park at the heart of Glasgow lies the Burrell Collection, home of the art treasures given to the city by Sir William Burrell. This film celebrates the spirit of that collection.

The film takes the form of a photomontage journey to the location of the Burrell Collection, with animated versions of its exhibits popping up along the way. Also of note is the music by Tom Rennie, who gives most of the animated figures their on distinctive sound.

More information, and a video of the complete film, can be found here.