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Aryl- and heteroarylcyclobutenone rearrangements proceed in excellent yield under continuous-flow conditions. The former shows a Hammett correlation with σI providing strong evidence that electrocyclisation is the rate-determining step and has a late transition state. The reaction has been modelled by using DFT and CCSD(T) methods, with the latter giving excellent correlation with the experimental rate constant. A short and efficient total synthesis of cribrostatin 6, an anti-neoplastic and anti-microbial agent, provides a topical demonstration of the value of this method.