Catalyzes the reversible phosphorolysis of sucrose into alpha-D-glucose 1-phosphate (Glc1P) and D-fructose (PubMed:14740189, PubMed:20691225). Is involved in sucrose degradation. Also displays transglucosylation activity in vitro, by transferring the glucosyl moiety of Glc1P to a broad range of monomeric sugars, such as D- and L-arabinose, D- and L-arabitol, and xylitol (PubMed:14740189). phosphate + sucrose = alpha-D-glucose 1-phosphate + D-fructose kcat is 207 sec(-1) for the phosphorolysis of sucrose (at 58 degrees Celsius and pH 6.5). Optimum pH is 6.0-6.5 for the phosphorolysis of sucrose. Optimum temperature is 48 degrees Celsius for the phosphorolysis of sucrose (PubMed:14740189). The His-tagged enzyme shows an optimum temperature of 58 degrees Celsius (PubMed:20691225). The immobilization of the enzyme on Sepabeads EC-HFA increases thermostability, and optimum temperature is shifted to 65 degrees Celsius (PubMed:20691225). Homodimer. Belongs to the glycosyl hydrolase 13 family. Sucrose phosphorylase subfamily.