Wolfson was director of Great Universal Stores (GUS) from 1973 to 1978 and from 1993 to 2000, and chairman from 1996 to 2000. The retailer had been founded by his uncle Isaac Wolfson as a mail order clothing company. He was first introduced to Margaret Thatcher by the Conservative Party treasurer Alistair McAlpine in 1975. In 1978 and 1979 he was Secretary to the Shadow Cabinet and between 1979 and 1985 Chief of Staff of the Political Office, 10 Downing Street. In that role he interviewed Bernard Ingham in 1979, before Ingham was made Thatcher's press secretary. The first official Chief of Staff in Number 10, he was the sole holder of the office until Jonathan Powell in 1997.