Catalysis of the reaction: 1,2-diacyl-3-O-(alpha-D-glucopyranosyl)-sn-glycerol + UDP-D-glucose = UDP + 1,2-diacyl-3-O-(alpha-D-glucopyranosyl(1,2)-O-alpha-D-glucopyranosyl)-sn-glycerol.
diglucosyl diacylglycerol (DGlcDAG) synthase activity