Arthur Edward Robert Gilligan was an English first-class cricketer who captained the England cricket team nine times in 1924 and 1925, winning four Test matches, losing four and drawing one. In first-class cricket, he played as an amateur, mainly for Cambridge University and Sussex, and captained the latter team between 1922 and 1929. A fast bowler and hard-hitting lower order batsman, Gilligan completed the double in 1923 and was one of Wisden's Cricketers of the Year for 1924. When his playing career ended, he held several important positions in cricket, including that of England selector and president of the Marylebone Cricket Club. A popular figure within cricket, he was widely regarded as sporting and friendly. During his playing days, Gilligan was a member of the British Fascists. He came to the notice of the Australian secret service during the 1924–25 MCC tour, and it is possible he helped to establish small fascist groups in Australia. It is unknown how long he remained a member, but the organisation practically ceased to exist by 1926.
Gilligan played cricket for Dulwich College before the First World War, then for Cambridge, twice winning his blue.