In the early 1970, Moberly was arrested after a demonstration outside Downing Street: the protest was against the British government's inaction over the war in Rhodesia. She had been accused of throwing a placard stating "No Peace Without Majority Rule" at a car containing the then prime minister, Ted Heath: she was convicted of a breach of the peace. She was defended by the eminent barrister Dingle Foot. Her conviction was overturned on appeal, due in part because the "Morning Star" published a photograph of her under arrest but still holding the placard in question.