Catalysis of the transfer of a solute or solutes from one side of a membrane to the other according to the reaction: glucose + H+ = glucose + H+. This activity is constitutive and therefore always present, regardless of demand. Symporter activity enables the active transport of a solute across a membrane by a mechanism whereby two or more species are transported together in the same direction in a tightly coupled process not directly linked to a form of energy other than chemiosmotic energy. In high affinity transport the transporter is able to bind the solute even if it is only present at very low concentrations.