The photochemical box-model CiTTyCAT is used to analyse the absence of oxygen mass-independent anomalies (O-MIF) in volcanic sulphates produced in the troposphere. An aqueous sulphur oxidation module is implemented in the model and coupled to an oxygen isotopic scheme describing the transfer of O-MIF during the oxidation of SO$_2$ by OH in the gas-phase, and by H$_2$O$_2$, O$_3$ and O$_2$ catalysed by TMI in the liquid phase. Multiple model simulations are performed in order to explore the relative importance of the various oxidation pathways for a range of plausible conditions in volcanic plumes. Note that the chemical conditions prevailing in dense volcanic plumes are radically different from those prevailing in the surrounding background air. The first salient finding is that, according to model calculations, OH is expected to carry a very significant O-MIF in sulphur-rich volcanic plumes and, hence, that the volcanic sulphate produced in the gas phase would have a very significant positive isotopic enrichment. The second finding is that, although H$_2$O$_2$ is a major oxidant of SO$_2$ throughout the troposphere, it is very rapidly consumed in sulphur-rich volcanic plumes. As a result, H$_2$O$_2$ is found to be a minor oxidant for volcanic SO$_2$. According to the simulations, oxidation of SO$_2$ by O$_3$ is negligible because volcanic aqueous phases are too acidic. The model predictions of minor or negligible sulphur oxidation by H$_2$O$_2$ and O$_3$, two oxidants carrying large O-MIF, are consistent with the absence of O-MIF seen in most isotopic measurements of volcanic tropospheric sulphate. The third finding is that oxidation by O$_2$/TMI in volcanic plumes could be very substantial and, in some cases, dominant, notably because the rates of SO$_2$ oxidation by OH, H$_2$O$_2$, and O$_3$ are vastly reduced in a volcanic plume compared to the background air. Only cases where sulphur oxidation by O$_2$/TMI is very dominant can explain the isotopic composition of volcanic tropospheric sulphate.