Stewart claimed bronze in the men’s points race but Tanfield came home fourth in the men’s individual pursuit while Barker finished sixth in the women’s omnium.
Stewart rode a tactically astute race as the 22-year-old Scot twice took a lap on the field to finish with 49 points, edging out Hong Kong’s King Lok Cheung by a single point for the final medal.
And he was delighted to get on the podium after a rough start to the year in which he has spent almost as much time in dentists’ waiting rooms than at the velodrome.
“I went in thinking I’d love a medal here but I wouldn’t be disappointed if I didn’t get on,” he said. “I’ve had a tough month. I’ve had a lot of dental work with abscesses. I’ve been to the dentist six times already this year so up until about a week ago I hadn’t had a good day.
“Then I started to feel like myself again and thought if I can get a medal I’ll be super happy.”
Australian Cameron Meyer comfortably defended his title with a total of 70 points while Jan Willem van Schip took the silver medal.
Barker had started the final event of the omnium, the points race, in the bronze medal position but did not have enough left in the tank to see it through.
Kirsten Wild took the rainbow jersey, a second gold of the championships for the Dutchwoman.
Twenty-four hours after helping Britain win gold in the men’s team pursuit, Tanfield ran out of gas to lose the bronze medal race in the individual pursuit to Russia’s Alexander Evtushenko.
The 21-year-old amateur started out strong, leading by over a second and a half at one point, but it turned out he had started too strongly and he faded badly down the stretch.
“I’m not hedging around here,” he said. “I came here to try to win. I was feeling good but tactically I sort of let myself down. But the main thing is I’ve learned from the experience.
“Hopefully next year I’ll come back stronger.”