Catalyzes the interconversion of D-glucose 1-phosphate (G1P) and D-glucose 6-phosphate (G6P), forming beta-D-glucose 1,6-(bis)phosphate (beta-G16P) as an intermediate. The beta-phosphoglucomutase (Beta-PGM) acts on the beta-C(1) anomer of G1P. Glucose or lactose are used in preference to maltose, which is only utilized after glucose or lactose has been exhausted. It plays 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. Competitively inhibited by alpha-D-galactose-1-phosphate. Optimum pH is around 7. Relatively stable in solution within the pH range of 5-9.5. Monomer. By maltose, trehalose and sucrose and repressed by glucose and lactose. Autophosphorylated. 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. Belongs to the HAD-like hydrolase superfamily. CbbY/CbbZ/Gph/YieH family.