Wolpert, who was born at Johannesburg in South Africa, trained initially as an engineer at the University of Witwatersrand. After working as an engineer in Britain and Israel, Wolpert's interests turned to biology and he began to study for a PhD in embryology at King's College, London. He taught there from 1958 until 1966, when he was appointed professor of biology at the Middlesex Hospital Medical School. From 1987 he has worked at University College, London.

Wolpert worked mainly on the problem of pattern formation in biological development. How is it, for example, that the same differentiated cells – muscle, cartilage, skin, connective tissue – arrange themselves as legs in one place and arms in another. Francis Crick proposed in 1970 that patterns could be produced through the action of a ‘morphogen’, a substance whose concentration throughout the field could be sensed by individual cells. Wolpert illustrated the mechanism with his flag analogy.

Imagine a line of cells capable of turning blue, red, or white. What simple mechanism could generate the pattern of the French tricolor? One way would be to have a chemical whose concentration, while fixed at one end of the line, decreased along the line. Cells could respond to a certain concentration of the morphogen and turn blue, red, or white accordingly.

Wolpert found that in such a system it should be possible to specify some 30 different cell states along a line of about 100 cells. The limiting factor was the accuracy with which cells can identify thresholds of concentration.

Wolpert identified a second positional system, one dependent upon time. Wing growth in chicks, for example, is mainly due to cell multiplication at the tip of the limb in a region known as the ‘progress zone’. The cells learn their position by responding to the length of time they remain in the progress zone. Thus the cells which stay in the progress zone the shortest time form the humerus, and those that stay in the longest develop into digits.

Much recent work in developmental biology was described by Wolpert in his The Triumph of the Embryo (Oxford, 1991), material that was originally presented in his 1986 Royal Institution Christmas Lectures. Wolpert also took it upon himself to speak for science in such works as his The Unnatural Nature of Science (London, 1993), against what he saw as increasingly philistine attacks from journalists and politicians against the aims and methods of modern science.