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. phosphate + uridine = alpha-D-ribose 1-phosphate + uracil Pyrimidine metabolism; UMP biosynthesis via salvage pathway; uracil from uridine (phosphorylase route): step 1/1. Homohexamer. The homohexamer shows 4-fold, 6-fold or 8-fold symmetry. Belongs to the PNP/UDP phosphorylase family.