Paddon's first full season at West Ham, by that point managed by John Lyall, saw 54 appearances and 4 goals. He featured all of the games in the successful 1974–75 FA Cup run, with the second goal of the 2–0 victory in the Final against Fulham scored by Alan Taylor after 'keeper Peter Mellor failed to deal with a shot by Paddon. The season also featured what Paddon described afterwards as "the best goal I've ever scored", a 40-yarder against Wolverhampton Wanderers that found the net with some help from the wind. He managed 5 goals in 57 appearances during the 1975–76 season, including every game of the European Cup Winners' Cup campaign. He scored from 30 yards in the first leg of the semi-final against Eintracht Frankfurt, but the team were only able to pick up a runners-up medal in the Final against Anderlecht. He made a total of 152 appearances, scoring 15 goals, in his three years at West Ham. His exploits that season resulted in him being voted runner-up for Hammer of the Year, behind Brooking.