The Campaign for Nuclear Disarmament, or CND, was an organisation formed to protest the hydrogen bomb.
The group was active in England in the late 1950s and early 1960s. At first they marched to Aldermaston, but later marched from Aldermaston to London. The marches were generally peaceful, and because they took place over a weekend, some churches allowed the marchers to stay overnight to rest from their journey.
In 1960, the Third Doctor and Jo Grant participated in the march because Jo had long wondered what it was like. She befriended Joan, an older woman who had participated in the march before. (PROSE: Come Friendly Bombs...)