Catalyzes the reversible phosphorylytic cleavage of uridine and deoxyuridine to uracil and ribose- or deoxyribose-1-phosphate (PubMed:26898674). The produced molecules are then utilized as carbon and energy sources or in the rescue of pyrimidine bases for nucleotide synthesis (Probable). phosphate + uridine = alpha-D-ribose 1-phosphate + uracil kcat is 35.9 sec(-1) for uridine. kcat is 0.41 sec(-1) for thymidine. Pyrimidine metabolism; UMP biosynthesis via salvage pathway; uracil from uridine (phosphorylase route): step 1/1. Homodimer. Belongs to the PNP/UDP phosphorylase family.