After honing his skills in the Irish Formula Ford Championship, Daly had his first drive in the European Formula Two Championship in 1977. In 1978 and 1979, he competed in both Formula Two and Formula One, finishing third in the Formula Two championship in both seasons. From 1980 to 1982, he focussed on Formula One, his best year being 1980, when he scored two fourth-place finishes and finished 11th in the Drivers' Championship. His two most memorable moments in F1 both came in the Monaco Grand Prix. In 1980 he crashed spectacularly at the first corner after vaulting three other cars. In 1982 he suddenly found himself in contention for the win when the four cars ahead of him ran into problems with under two laps to go, but ended up on the sidelines himself when his gearbox seized moments later.