Catalysis of the reaction: beta-D-galactosyl-(1,4)-D-glucosylceramide + UDP-galactose = alpha-D-galactosyl-(1,4)-beta-D-galactosyl-(1,4)-D-glucosylceramide + UDP.
Gal-beta-(1,4)-Glc-beta-1-Cer alpha-(1,4)-galactosyltransferase activity