Co-immobilisation of three separate multiple blue copper oxygenases, a Myceliophthora thermophila laccase, a Streptomyces coelicolor laccase and a Myrothecium verrucaria bilirubin oxidase, with an [Os(2,2′-bipyridine)2(polyvinylimidazole)10Cl]+/2+ redox polymer in the presence of multi-walled carbon nanotubes (MWCNTs) on graphite electrodes results in enzyme electrodes that produce current densities above 0.5 mA cm−2 for oxygen reduction at an applied potential of 0 V versus Ag/AgCl. Fully enzymatic membraneless fuel cells are assembled with the oxygen-reducing enzyme electrodes connected to glucose-oxidising anodes based on co-immobilisation of glucose oxidase or a flavin adenine dinucleotide-dependent glucose dehydrogenase with an [Os(4,4′-dimethyl-2,2′-bipyridine)2(polyvinylimidazole)10Cl]+/2+ redox polymer in the presence of MWCNTs on graphite electrodes. These fuel cells can produce power densities of up to 145 μW cm−2 on operation in pH 7.4 phosphate buffer solution at 37 °C containing 150 mM NaCl, 5 mM glucose and 0.12 mM O2. The fuel cells based on Myceliophthora thermophila laccase enzyme electrodes produce the highest power density if combined with glucose oxidase-based anodes. Although the maximum power density of a fuel cell of glucose dehydrogenase and Myceliophthora thermophila laccase enzyme electrodes decreases from 110 μW cm−2 in buffer to 60 μW cm−2 on testing in artificial plasma, it provides the highest power output reported to date for a fully enzymatic glucose-oxidising, oxygen-reducing fuel cell in artificial plasma.