Reversibly phosphorolyzes beta-D-galactosyl-(1->4)-L-rhamnose to form alpha-D-galactose 1-phosphate and L-rhamnose. Does not phosphorolyze galacto-N-biose or lacto-N-biose. In the reverse reaction, has the highest activity toward L-rhamnose, also has activity toward L-mannose, and low activity toward L-lyxose, D-glucose, 2-deoxy-D-glucose and D-galactose. beta-D-galactosyl-(1->4)-L-rhamnose + phosphate = alpha-D-galactose 1-phosphate + L-rhamnopyranose Belongs to the glycoside hydrolase 112 family.