Lightweights Sam Maxwell and Josh Taylor are through to the quarter-finals of the final Olympic qualifying tournament in Trabzon, Turkey.
Liverpool's Maxwell beat Moldova's Piotr Apostol 20-10 and Taylor beat Latvia's Artjoms Ramlavs 14-4.
Maxwell and Taylor need to make the final, or lose in the semi-finals to the eventual winner, to reach London, although only one can qualify.
But London light-flyweight Charlie Edwards' hopes are over after he lost.
Edwards' hopes of starring in his home Olympics were shattered by a 17-12 defeat to Bulgaria's Aleksander Aleksandrov.
Heavyweight Warren Baister, light-heavyweight Callum Smith and middleweight Anthony Ogogo also remain in the tournament.
Five GB boxers have already qualified for the 2012 Olympics. They are Andrew Selby, Luke Campbell, Tom Stalker, Fred Evans and Anthony Joshua.