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