Allgårdh won the Swedish junior title in 1979 and 1981. He reached the quarter-finals at the junior tournament of the French Open in 1984 and the second round at the Wimbledon junior tournament by defeating Thomas Muster . In 1983 he became a professional tennis player and initially played on the ATP Challenger Tour . He was in the finals of the Challenger tournaments in Bergen , Knokke-Heist , Tampere and Hanko . In 1987 he won his first double title on the ATP World Tour at the side of Ulf Stenlund in Bari . In 1992 his second and last title followed in Guarujá . He achieved his highest scores in the tennis world rankings in 1988 with position 101 in singles and 1991 with position 93 in doubles.
In the individual, he could never qualify for a Grand Slam tournament . His best results in doubles were second round participation at the French Open and Wimbledon in 1993.
After the end of his professional career, he played on the ATP Seniors Circuit in 2003, where he achieved position 45 as the best ranking.