Catalysis of the transfer of N-acetylglucosamine (GlcNAc) in a beta-1,3 linkage to the mannose(beta-1,4)Glc disaccharide core of glycolipids.
UDP-N-acetylglucosamine:beta-D-mannosyl-glycolipid beta-1,3-N-acetylglucosaminyltransferase activity