Catalyzes the interconversion through a 2-keto intermediate of uridine diphosphogalactopyranose (UDP-GalP) into uridine diphosphogalactofuranose (UDP-GalF) which is a key building block for cell wall construction in Mycobacterium tuberculosis. UDP-alpha-D-galactose = UDP-alpha-D-galactofuranose Cell wall biogenesis; cell wall polysaccharide biosynthesis. Homotetramer. Belongs to the UDP-galactopyranose/dTDP-fucopyranose mutase family.