The sitcom takes place in a BBC studio in 1961, where a group of "bright young things" and aging actors produce a futuristic drama set in the year 2006, containing space flight, ray guns, and contact with aliens.
The "comic relief" for the radio production is provided by a stereotypical Welshman, "Taffy" Jones, played by a non-Welsh actor, Douglas Bennings (Jon Glover).
However, the BBC decides that thanks to the Soviet Union's apparent lead in space travel, national morale requires it to continue with a new pro-British, anti-Soviet slant.
BBC executive Godfrey Winnard (John Fortune) watches over the new production and keeps adding new elements to the mix, such as a member of the Royal Shakespeare Company (Leslie Phillips) brought in to play an android.
Faced with mobs of angry Welsh fans calling him "Taffy killer," Hugo writes in a resurrection for the character, but Douglas's "more authentic" reading of the part causes the disgusted locals to cut power to the studio, which the team interprets as the arrival of Armageddon.