Catalysis of the reaction: 4-beta-D-galactosyl-O-beta-D-xylosylprotein + UDP-galactose = 3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xylosylprotein + UDP.
uridine diphosphogalactose-galactosylxylose galactosyltransferase activity