He was known for riding the horse Red Rum to win the Grand National in 1973 and 1974 and for second place in 1975. He first won the Grand National at the age of 20, in 1968 riding Red Alligator. He retired in 1976 with a head injury. Fletcher is one of the only jockey to have won the Grand National three times. He won the Scottish National in 1974. His record winning time on Red Rum in the 1973 Grand National was to stand for 17 years till beaten by Mr Frisk ridden by Marcus Armytage. 