Catalysis of the reaction: beta-D-galactosyl-(1,4)-beta-N-acetyl-D-glucosaminyl-R + UDP-galactose = alpha-D-galactosyl-(1,3)-beta-D-galactosyl-(1,4)-beta-N-acetyl-D-glucosaminyl-R + UDP.
UDP-Gal:beta-D-Gal(1,4)-D-GlcNAc alpha-(1,3)-galactosyltransferase activity