The high selectivity of biocatalysis offers a valuable method for greener, more efficient production of enantiopure molecules. Operating immobilised enzymes in flow reactors can improve the productivity and handling of biocatalysts, and using H2 gas to drive redox enzymes bridges the gap to more traditional metal‐catalysed hydrogenation chemistry. Herein, we describe examples of H2‐driven heterogeneous biocatalysis in flow employing enzymes immobilised on a carbon nanotube column, achieving near‐quantitative conversion in <5 min residence time. Cofactor recycling is carried out in‐situ using H2 gas as a clean reductant, in a completely atom‐efficient process. The flow system is demonstrated for cofactor conversion, reductive amination and ketone reduction, and then extended to biocatalytic deuteration for the selective production of isotopically labelled chemicals.