Beta-galactosyltransferase that transfers beta-galactose to hydroxylysine residues of type I collagen. By acting on collagen glycosylation, facilitates the formation of collagen triple helix. (5R)-5-hydroxy-L-lysyl-[collagen] + UDP-alpha-D-galactose = (5R)-5-O-(beta-D-galactosyl)-5-hydroxy-L-lysyl-[collagen] + H(+) + UDP Belongs to the glycosyltransferase 25 family.