Brees totaled 338 yards on 30 completions in 41 attempts against his former team.
The contest, latest in the NFL's international showcase program, was played at Wembley Stadium.
Brees has thrown for at least 300 yards in six of eight games this season.
Deuce McAllister carried 18 times for 55 yards and a score for the Saints (4-4).
San Diego quarterback Philip Rivers also tossed three touchdown passes, finishing 25-of-40 for 341 yards and an interception.
LaDainian Tomlinson ran 19 times for 105 yards and caught five passes for 65 yards and a touchdown for the Chargers (3-5).
Antonio Gates and Vincent Jackson caught Rivers' other two scoring tosses.