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Abstract The growing experimental indication of Lepton Flavour Universality Violation (LFUV) both in charged- and neutral-current semileptonic B-decays, has triggered many theoretical interpretations of such non-standard phenomena. Focusing on popular scenarios where the explanation of these anomalies requires New Physics at the TeV scale, we emphasise the importance of including electroweak corrections to obtain trustable predictions for the models in question. We find that the most important quantum effects are the modifications of the leptonic couplings of the W and Z vector bosons and the generation of a purely leptonic effective Lagrangian. Although our results do not provide an inescapable no-go theorem for the explanation of the B anomalies, the tight experimental bounds on Z-pole observables and τ decays challenge an explanation of the current non-standard data. We illustrate how these effects arise, by providing a detailed discussion of the running and matching procedure which is necessary to derive the low-energy effective Lagrangian.