This is one of my favourite sketches by David Mitchell & Robert Webb, in which they use one of their trademark ironic devices. Their characters are idiots. But the blithe, cheery manner in which they express their idiotic thoughts contrasts sharply with the cold precision of the words they use, exposing the wrongheadedness of their ideas with a skill of articulation and detachment that the characters would never possess in reality. The result is a devastatingly funny sketch that works like a well-oiled piece of Swiss chocolate.
This is an audio recording of the TV version of the sketch, which was first broadcast on That Mitchell and Webb Look on 10 October 2006. There is also a radio version, from Radio 4's That Mitchell and Webb Sound (the linked radio recording does not contain the Touching Cloth sketch). In the TV series they shamelessly (but successfully) rehashed many of their old radio sketches.
Touching Cloth (streaming audio)