Catalyzes the conversion of UDP-glucose into UDP-glucuronate, one of the precursors of teichuronic acid. H2O + 2 NAD(+) + UDP-alpha-D-glucose = 3 H(+) + 2 NADH + UDP-alpha-D-glucuronate Competitively inhibited by UDP-glucose. Activated by phosphorylation, which may increase affinity for NAD(+); inhibited by dephosphorylation. Nucleotide-sugar biosynthesis; UDP-alpha-D-glucuronate biosynthesis; UDP-alpha-D-glucuronate from UDP-alpha-D-glucose: step 1/1. Phosphorylated on tyrosine residue(s). Phosphorylated by YwqD and dephosphorylated by YwqE in vitro. Belongs to the UDP-glucose/GDP-mannose dehydrogenase family.