Born in Dunedin on 13 April 1915, Begg was the younger son of surgeon Charles Mackie Begg and Lillian Helen Lawrance Begg, and nephew of Robert Campbell Begg. His father served throughout World War I, becoming the senior medical officer with the New Zealand Expeditionary Force, but contracted influenza and pneumonia and died at Twickenham, London, in February 1919. Begg and his mother and brother, who had travelled to England at the end of the war, then returned to New Zealand. Begg was educated at John McGlashan College in Dunedin, and then studied medicine at the University of Otago, graduating MB ChB in 1941. A tall man, Begg was an all-round sportsman, and represented the university at cricket, golf and skiing. On 11 April 1942, Begg married Margaret Milne "Margot" MacLean, a librarian, at Dunedin. She was a granddaughter of John Shand, one of the foundation professors of the University of Otago. The couple went on to have four children.
A right-arm medium pace bowler and a tail-end batsman, Begg played three first-class matches for Otago in the 1939/40 and 1940/41 seasons. He took five wickets, at an average of 47.60, with best bowling figures of 2 for 43. With the bat, he made a total of 30 runs in four innings including one not out, with a high score of 16 and an average of 10.00. Begg played one match for New Zealand Services, on 12 July 1945, against P.F. Warner's XI at Lord's, bowling 11 overs without success and scoring 1 not out with the bat.
Medical career
Between 1946 and 1948, Begg trained in paediatrics in London, Edinburgh and Stockholm, earning a diploma in child health in 1947, and membership of the Royal College of Physicians and the Royal College of Physicians of Edinburgh in 1948. Returning to Dunedin the following year, he was appointed as a paediatrician at Dunedin Public Hospital, Queen Mary Maternity Hospital, and the Karitane-Harris Hospitial in Andersons Bay. He was also a lecturer in paediatrics at the Otago Medical School from 1949 to 1976. An admirer of Sir Truby King, Begg served as medical director of the Plunket Society between 1956 and 1977, and was a leading advocate for preventive medicine. He campaigned for the fluoridation of public water supplies, the eradication of hydatids and bovine tuberculosis, and the development of a milk biscuit for protein-deprived children in developing countries. Between 1971 and 1976 he served as the medical advisor to the New Zealand Food Bank, which distributed the biscuits overseas. His parental reference book, The New Zealand child and his family, was published in 1970. Begg gave service to various professional bodies, as president of the Paediatric Society of New Zealand, chair of the council of the New Zealand branch of the British Medical Association from 1964 to 1966, and president of the New Zealand Medical Association in 1974.
Historian
Begg and his brother Charles became experts on the history of Fiordland. Their first book, Dusky Bay, was published in 1966 and won the Hubert Church Memorial Award for prose. This was followed by the publication of James Cook and New Zealand in 1969, Port Preservation in 1973, and The World of John Boultbee in 1979. He served on the council of the New Zealand Historic Places Trust from 1970 to 1978, and as the trust's chair between 1978 and 1986.
