Undy was born on 2 November 1938 in Nottingham into a Labour-supporting, non-conformist, working-class family who were often trade unionists; his father Harold was a fitter and his mother Harriet (née Holmes) was a housewife.
Undy failed the Eleven-plus examination and attended Huntingdon Street secondary modern school before leaving aged 15 to become an apprentice fitter.
He successfully applied for a Trades Union Congress scholarship to Ruskin College, Oxford, and completed a two-year diploma in social studies there in 1969.
He then spent three years at Wadham College, Oxford, as an undergraduate, and left with a Bachelor of Arts degree in history and economics in 1972.
In 1994, he was also appointed a University Lecturer at the Saïd Business School, where he subsequently became a reader in management studies.