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