A sprinter and long jumper since he was young, he continued to sport while studying in Cambridge, which earned him a spot in the 1920 Olympic team. These Games were no great success; Abrahams was eliminated in the quarter-finals of both the 100 m and 200 m, and he finished 20th in the long jump. As a part of the British relay team, he took fourth place in the 4 x 100 m.
After dominating the national long jump and sprint events, Abrahams was an outsider for the medals at the 1924 Olympics in Paris, France. He won the 100 m, beating all the American favourites. In the 200 m, he reached the final, in which he ranked sixth and last. As an opening runner for the 4 x 100 m team, Abrahams won a second Olympic medal, a silver one; Abrahams did not compete in the long jump.
A foot injury forced Abrahams to end his career the following year. He subsequently served as an athletics journalist for forty years, also commentating the sport for the BBC radio.