  Motivated by the recent experimental progress on the $R_{D^{(\ast)}}$ and
$R_{K^{(\ast)}}$ anomalies in $B$-decays, we consider an extension of the
Standard Model by a single vector leptoquark field. We study how one can
achieve the required lepton flavour non-universality, starting from a priori
universal gauge couplings. While the unitary coupling flavour structure,
induced by the mass misalignment of quarks and leptons after $SU(2)_L$
breaking, does not allow to comply with stringent bounds from lepton flavour
violating processes, we find that effectively non-unitary couplings, due to
mixings with heavy vector-like fermions, hold the key to simultaneously address
the $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$ anomalies. Furthermore, in the near
future, the expected progress in the sensitivity on charged lepton flavour
violating observables should allow to probe a large region of the preferred
parameter space in this class of vector leptoquark models.
