Catalyzes the reversible isomerization of alpha-D-glucose 1- phosphate to alpha-D-glucose 6-phosphate (PubMed:15378030, PubMed:25288802). The mechanism proceeds via the intermediate compound alpha-D-glucose 1,6-bisphosphate (Probable) (PubMed:25288802). This enzyme participates in both the breakdown and synthesis of glucose (PubMed:17924679, PubMed:25288802). {ECO:0000269|PubMed:15378030, ECO:0000269|PubMed:17924679, ECO:0000269|PubMed:25288802, ECO:0000305|PubMed:15378030}. This is the function of PGM1 (phosphoglucomutase 1, ENSG00000079739).