Regarded as "one of the most exciting players of the mid-seventies", and "one of the men most likely to succeed when he turned professional", Fagan turned professional in October 1976. He made his first maximum break on 15 January 1977, his 26th birthday, against Dave Gilbert at the Clapton Bus Garage Social Club. At the 1977 World Snooker Championship, he beat Jim Meadowcroft 11–9 in qualifying and then lost 7–13 to defending champion Ray Reardon in the last 16, having finished the first session of the match level at 4–4 and the second 7–10 behind. Reardon then won all three in the final session, taking the last two of them on the black. The matches between Fagan and Reardon, and between Fred Davis and John Pulman, were the first to be held at the Crucible Theatre, which as of March 2020 had remained as the venue for the World Snooker Championship for 43 years.