Smith was born in Stoke Newington, London, and began running competitively in the 1950s, at which time the longest distance for women in international competitions was 800 meters. She won the English National Crosscountry Championship (AAA) in 1959 and 1960. In 1965, she told Athletics Weekly that she intended to continue competing "for two more years at the most" and stopped running competitively in 1968.
Smith returned to competitive running in 1969, and broke the world record for the 3000 metres distance in 1971, and won the bronze medal in 1971, the gold medal in 1972 and the silver medal in 1973 in the IAAF World Cross Country Championships. She reached the semi-final of the 1500 metres at the 1972 Olympic Games. In 1973, she won her third National Crosscountry Championship. She won the bronze medal in 3000 m at the European Athletics Championships in 1974.
In 1978, she retired from track running after setting a new world record for 3000 m in the age group W40 of 9:11.2 minutes, which was broken 27 years later, and ran her first marathon in 1979, beating the previous British record held by Rosemary Cox by nine minutes and seventeen seconds in a time of 2:41:37.
In 1979, she won the Avon International Marathon in Waldniel. In 1979 and 1980, she won the first two editions of the Tokyo International Women's Marathon. In 1980, she set a new British 25 kilometre record of 1:28:18 in Bruges, which was also the new W40 world record which was broken 24 years later.
In 1981, she won the first London Marathon in 2:29:57, becoming the first British woman and the first woman over 40 to complete the distance in less than two and a half hours. A year later, she won the event in 2:29:43, again setting a new British record, and becoming the oldest woman to win the race at 44 years, 195 days, a record which has not yet been broken.
In the first World Athletics Championships in 1983 in Helsinki, she finished ninth in the marathon. In 1984, she became the oldest female Olympic athlete by running in the first women's Olympic marathon, and finished eleventh at the age of 46.
She retired from competitive running in 1986 after setting a new W45 record for the ten mile distance of 55:33.
In 1984, Smith was awarded the MBE. She and her husband, Bryan, are on the board of trustees of the London Marathon Charitable Trust. Bryan is a marathon coach who also organises the Mini London Marathon.