Catalyzes the conversion of beta D-glucose 1-phosphate (G1P) to D-glucose 6-phosphate (G6P), forming beta-D-glucose 1,6-(bis)phosphate (beta-G16P) as an intermediate (PubMed:16990279, PubMed:29684280) (Probable). Phosphatase activity with the reaction intermediate beta-G16P has been measured (PubMed:25848029). In vitro interconverts beta D-glucose 1-phosphate, beta-D-allose 1-phosphate, beta-D-galactose 1-phosphate and beta-D-mannose 1-phosphate to their corresponding sugar 6-phosphate product. The beta-D-glucose 1-phosphate substrate may be furnished by YcjT (AC P77154), the apparent upstream enzyme in the putative biochemical pathway encoded in this locus (yjcM to ycjW) (PubMed:29684280). It may play a key role in the regulation of the flow of carbohydrate intermediates in glycolysis and the formation of the sugar nucleotide UDP-glucose. beta-D-glucose 1-phosphate = beta-D-glucose 6-phosphate Binds 2 magnesium ions per subunit. kcat is 21 sec(-1) for conversion of G1P to G6P, kcat is 0.5 sec(-1) for conversion of G6P to G1P. Monomer. Autophosphorylated. Cells lacking this gene are only slightly more susceptible to nalidixic acid, but are more sensitive to UV irradiation than the wild-type (PubMed:20128927). No visible phenotype when grown on glucose (PubMed:29684280). The catalysis proceeds via a phosphoenzyme formed by reaction of an active-site nucleophile with the cofactor glucose 1,6-diphosphate (G1,6-diP). The phosphorylated mutase binds either G1P or G6P and transfers the phosphoryl group to the C(6)OH or C(1)OH, respectively (By similarity). Belongs to the HAD-like hydrolase superfamily. CbbY/CbbZ/Gph/YieH family.