Context. One of the important questions of astrochemistry is how complex organic molecules, including potential prebiotic species, are formed in the envelopes around embedded protostars. The abundances of minor isotopologues of a molecule, in particular the D- and ¹³C-bearing variants, are sensitive to the densities, temperatures and timescales characteristic of the environment in which they form, and can therefore provide important constraints on the formation routes and conditions of individual species. Aims. The aim of this paper is to systematically survey the deuteration and the ¹³C content of a variety of oxygen-bearing complex organic molecules on solar system scales toward the “B component” of the protostellar binary IRAS16293–2422. Methods. We have used the data from an unbiased molecular line survey of the protostellar binary IRAS16293−2422 between 329 and 363 GHz from the Atacama Large Millimeter/submillimeter Array (ALMA). The data probe scales of 60 AU (diameter) where most of the organic molecules are expected to have sublimated off dust grains and be present in the gas phase. The deuterated and ¹³C isotopic species of ketene, acetaldehyde and formic acid, as well as deuterated ethanol, are detected unambiguously for the first time in the interstellar medium. These species are analysed together with the ¹³C isotopic species of ethanol, dimethyl ether and methyl formate along with mono-deuterated methanol, dimethyl ether and methyl formate. Results. The complex organic molecules can be divided into two groups with one group, the simpler species, showing a D/H ratio of ≈2% and the other, the more complex species, D/H ratios of 4–8%. This division may reflect the formation time of each species in the ices before or during warm-up/infall of material through the protostellar envelope. No significant differences are seen in the deuteration of different functional groups for individual species, possibly a result of the short timescale for infall through the innermost warm regions where exchange reactions between different species may be taking place. The species show differences in excitation temperatures between 125 and 300 K. This likely reflects the binding energies of the individual species, in good agreement with what has previously been found for high-mass sources. For dimethyl ether, the ¹²C/¹³C ratio is found to be lower by up to a factor of 2 compared to typical ISM values similar to what has previously been inferred for glycolaldehyde. Tentative identifications suggest that the same may apply for ¹³C isotopologues of methyl formate and ethanol. If confirmed, this may be a clue to their formation at the late prestellar or early protostellar phases with an enhancement of the available ¹³C relative to ¹²C related to small differences in binding energies for CO isotopologues or the impact of FUV irradiation by the central protostar. Conclusions. The results point to the importance of ice surface chemistry for the formation of these complex organic molecules at different stages in the evolution of embedded protostars and demonstrate the use of accurate isotope measurements for understanding the history of individual species.