Making his Test debut in 1953 at home against New Zealand, he had only 9 first-class games to his name. He finished the series with 24 wickets, including 8 for 87 in his second Test.
Adcock was the Wisden Cricketer of the Year in 1961. The previous year in South Africa's tour of England he took 26 wickets in the Tests and 108 wickets in total at an average of 14. It was a controversial tour with his bowling partner Geoff Griffin being no-balled for throwing.
After retiring from cricket he became a radio commentator.