A 1,3‐dipolar cycloaddition reaction of carbohydrate‐derived five‐membered cyclic ketonitrones with alkynes and alkenes was developed as an efficient and regioselective process to access highly functionalised isoxazolines and isoxazolidines bearing a quaternary centre α to the nitrogen atom. The latter compounds were used as intermediates for the synthesis of unprecedented ring‐junction‐substituted polyhydroxylated pyrrolizidines and indolizidines. These compounds were evaluated against a panel of glycosidases, and showed moderate but selective inhibition of α‐glucosidases.