David studied chemical engineering at Imperial College at both undergraduate and graduate levels, receiving his PhD in 1983. Following this, he worked on modelling and control projects for British Gas before taking a position as lecturer at the University of Adelaide, a position he held from 1986 until 1990.

David joined UCL as a lecturer in 1990. He was appointed professor in 2000. In 2005, he was appointed Head of the UCL Graduate School and in 2014 Pro-Vice-Provost of the Doctoral School and Early Career Researchers. From 2008 until 2025, he was chair of the Steering Group of the League of European Research Universities (LERU) Doctoral Studies Policy Group.

In 2005, he was elected a Fellow of the Royal Academy of Engineering. He was Technical Programme Director for the 2005 World Congress of Chemical Engineering and was awarded the IChemE Council medal. He was awarded the Villermaux Medal of the European Federation of Chemical Engineers (EFCE) in 2023. He was President of IChemE for 2022–2023 and Scientific Vice President of the EFCE for 2018–2021. He retired from UCL in September 2024 and was appointed Emeritus Professor of Chemical Engineering.