In the event , Labour lost the 1959 election .
It voted at its 1960 Conference for unilateral nuclear disarmament , which represented CND 's greatest influence and coincided with the highest level of public support for its programme .
In the event , Labour lost the 1959 election , but it voted at its 1960 Conference for unilateral nuclear disarmament , which represented CND 's greatest influence and coincided with the highest level of public support for its programme .