Steel was born in Kirkcaldy, Fife, the son of a Church of Scotland minister also called David Steel, who would later serve as Moderator of the General Assembly of the Church of Scotland.
Lord Steel född i Kirkcaldy, Fife, var son till en präst i Skotska kyrkan också han vid namn David Steel, som senare skulle fungera som moderator i Skotska kyrkans generalförsamling.