After studying in Manchester and designing emergency buildings during the Second World War, Sir Leslie was appointed deputy architect at London County Council in charge of the design of the Royal Festival Hall.
Although traditionally clad in Portland stone, the festival hall was hailed as a triumph of modern movement architecture, as the auditorium floats effortlessly above spacious foyers. Begun in 1948, it was completed in 1951 in time for its role in the Festival of Britain.
Sir Leslie's major buildings included the zoology building for Oxford University in 1971, the Gulbenkian Foundation of Modern Art in Lisbon in 1984, and the Glasgow Concert Hall in 1984.
Although an early convert to modernism, Sir Leslie abjured fashionable imagery, believing that "ideas generate forms, and by consistently developing and elaborating these we build up a language". His architecture tended to be scaleless and monolithic externally.
During the 1960s, he drew up plans for the wholesale – though abortive – redevelopment of Whitehall and Bloomsbury.
In 1956, a year before he was knighted, he was appointed as Cambridge University's first professor of architecture. At Cambridge, he founded the Centre for Land Use and Built Form, since renamed the Martin Centre, which conducted research into the most efficient configurations of buildings.
One research project exposed the fallacy of tower blocks by demonstrating that continuous "ribbon" buildings one-third of the height occupy no more land area.