Catalyzes both the (1) reversible phosphorolysis of 2-O-alpha-D-glucopyranosyl-sn-glycerol (GG) from beta-D-glucose 1-phosphate (betaGlc1P) and glycerol and (2) the hydrolysis of betaGlc1P. the betaGlc1P hydrolysis is a glucosyl-transfer reaction to an acceptor water molecule that produces an anomer-inverted alpha-glucose, not a phosphatase-type reaction. In the absence of glycerol produces alpha-D-glucopyranose and phosphate from beta-D-glucopyranose 1-phosphate. 2-O-(alpha-D-glucopyranosyl)glycerol + phosphate = beta-D-glucose 1-phosphate + glycerol kcat is 95 sec(-1) with 2-O-alpha-D-glucopyranosyl-sn-glycerol. Optimum pH is 6.0-8.0. Homodimer. Belongs to the glycosyl hydrolase 65 family.