Welsh flyweight Andrew Selby had to settle for a bronze medal at the World Championships after losing his semi-final to Uzbekistan's Jasurbek Latipov.
England middleweight Antony Fowler was withdrawn from his semi-final in Almaty because of a hand injury.
The home nations' tally of two bronze medals compares to three silver and one bronze in 2011.
Jason Quigley became the first Irishman to reach a world final by defeating Russia's Artem Chebotarev.
Donegal boxer Quigley will take on home favourite Zhanibek Alimkhanuly in the middleweight final on Saturday.
Joe Ward won a bronze after being outboxed by Cuba's Julio Cesar la Cruz in his light-heavyweight semi-final.
GB Boxing chief Rob McCracken said he was encouraged by the performance of his inexperienced squad following the loss of a several Olympians.
"It is early days in the Olympic cycle so to come away with two medals is a very good outcome and a better result than we achieved at the same point four years ago," said McCracken.
"Andrew Selby was very unlucky and could easily have got the decision after boxing well in all three rounds.
"And, in only his second major championship, Antony Fowler demonstrated that he has what it takes to win medals at the highest level.
"Overall, it has been a good learning experience for a lot of the younger boxers and they will go away with a clearer sense of what it takes to become an elite international boxer."
Double European champion Selby, 25, was left heartbroken at the World Championships two years ago when he lost his final by a point.
And the Barry man, the top seed, was unlucky again in Almaty, having looked to have done enough to beat fourth seed Latipov.
Unseeded Liverpudlian Fowler, 22, was to have fought home fighter Zhanibek Alimkhanuly in his semi-final.
But he suffered a heavily bruised right hand in his quarter-final win over German Stefan Haertel.
"I am absolutely gutted, I felt I could have gone all the way," said Fowler, who damaged the same hand in 2012.