Dennis Taylor also beat Fagan in the quarter-finals of the 1979 UK Championship, 9–6, after Fagan had knocked out Mike Hallett 9–4 and Graham Miles 9–5. In the 1980 World Snooker Championship Fagan lost in his first match, 6–10 to Steve Davis. This was the last time he reached as far as the quarter-final of a major tournament other than the Irish Professional Championship or the 1986 Irish Masters, the latter resulting from a walkover against Kirk Stevens. He lost to Dennis Taylor in a challenge for the Irish Professional Championship in 1981, coming from 0–3 down to lead 5–4 at the end of the first session, and 10–8 at the close of the second session. The third session saw Fagan make a break of 107 on his way to building a 15–12 lead. However, Taylor retained the title, winning 22–21.