Smith was born in Liverpool and trained there throughout his career under coach Mike Holmes. Standing 1.85 meters tall (6 ft. 1 inch), Smith is considered "small" in comparison to most world-class high jumpers. He jumps off his left leg. He first emerged as a talented jumper in 1990 when he cleared 2.25 (7 ft 4 inches) at a British national meet in Gateshead. In 1991 he improved to 2.29, and then had his "breakout" year in 1992, improving his best by an astonishing 8 centimetres. He qualified for the 1992 Olympics in Barcelona and reached the finals, finishing in 12th place with a disappointing height of only 2.24. One month after those Olympics, he competed at the 1992 World Junior Championships, where he won, and equalled the junior world record of 2.37 metres (outdoors), which Dragutin Topic had achieved in 1990. Smith equalled this result twice more (once indoors and once outdoors.) He established his personal best of 2.38, set indoors at Wuppertal, Germany, on 4 February 1994, which still stands as the British record.