Dowdeswell grew up in Rhodesia and attended from 1967 to 1972, the Prince Edward School in Harare. His studies at the University of Witwatersrand in Johannesburg, he completed in 1978 with a Bachelor of Commerce degree. After that he moved to Switzerland. In 1974, he won his first doubles title in Dublin, the year after he won his only singles title. Between 1976 and 1980 he served on the Board of ATP. In 1981 he returned to England, where in 1984 he won the national tennis championship, what was it previously succeeded already in Switzerland and in Rhodesia.
Between 1981 and 1983 Dowdeswell had retired from the sport of tennis and worked on the London Stock Exchange. When he reached his comeback in 1983 after wins over Kevin Curren and Vitas Gerulaitis the finale of Johannesburg, where he was defeated in five sets against Johan Kriek. Between 1984 and 1990 he sat again on the Board of ATP. Throughout his career he has won eleven doubles titles. Its highest listing in the tennis world ranking he reached in 1983 with position 31 in the singles and in 1984 with position 24 in doubles.
His best individual result at a Grand Slam tournament was the two-time reaching the second round at the U.S. Open. In the doubles competition in 1975, he stood in the doubles final of Wimbledon, before these were Mike Davies and Bobby Wilson in 1960. Alongside Alan Stone Dowdeswell lost to Vitas Gerulaitis and Sandy Mayer. In 1976, he was with Chris tile in the semifinals of the U.S. Open. In mixed he stood at the side of Boshoff Delina in the final of the French Open in 1976, but they lost Ilana Kloss and Kim Warwick in three sets. In 2002 he succeeded together with Buster Mottram winning the title at Wimbledon in the OB 45 doubles competition against the defending champion Peter Fleming and Sandy Mayer.
Dowdeswell played in 1976, first for the Rhodesian Davis Cup team. From 1984 to 1986 he played for the British Davis Cup team. His greatest success with the British team was participating in the quarterfinals of the World Group in 1986, which Australia won 4-1. He lost it on the side of Jeremy Bates, the double match against John Fitzgerald and Pat Cash.
In 1986 he retired to his eleventh title win in the doubles competition final from the professional tennis back and graduated with a Master of Business Administration from the European Business School Paris. Since 1994 he has been with Merrill Lynch, where he worked as First Vice President since 2004. He is married and has three children.