Andrews began his career as an apprentice with Luton Town in the late 1950s, turning professional in 1960 but leaving the following year without making a first team appearance having suffered from homesickness. He continued his career at non-league level with Lower Gornal Athletic in 1961, reaching the Football League in October 1965 after signing for Cardiff City, along with Gary Bell for a fee of £2,100, a record transfer fee for Gornal that still stands, having been spotted by manager Jimmy Scoular. He made his first team debut just a few days later in a 2–1 defeat against Portsmouth, before scoring his first goal for the club a week later in a second 2–1 defeat against Bolton Wanderers. He went on to finish his first professional season with 20 goals in all competitions and scored 6 in the opening 12 matches of the following season before being displaced by new signing Bobby Brown and was allowed to leave to join Southport for £6,000 in February 1967, a club record fee at the time.