  The discrepancies between the measurements of rare (semi-)leptonic $B$ decays
and the corresponding Standard Model predictions point convincingly towards the
existence of new physics for which a heavy neutral gauge boson ($Z^\prime$) is
a prime candidate. However, the effect of the mixing of the $Z^\prime$ with the
SM $Z$, even though it cannot be avoided by any symmetry, is usually assumed to
be small and thus neglected in phenomenological analyses. In this letter we
point out that a mixing of the naturally expected size leads to lepton flavour
universal contributions, providing a very good fit to $B$ data. Furthermore,
the global electroweak fit is affected by $Z-Z^\prime$ mixing where the tension
in the $W$ mass, recently confirmed and strengthened by the CDF measurement,
prefers a non-zero value of it. We find that a $Z^\prime$ boson with a mass
between $\approx 1-5\,\rm {TeV}$ can provide a unified explanations of the $B$
anomalies and the $W$ mass. This strongly suggests that the breaking of the new
gauge symmetry giving raise to the $Z^\prime$ boson is linked to electroweak
symmetry breaking with intriguing consequences for model building.
