Motivated by the intriguing discrepancies in $b\to s\ell \ell$ transitions, the fermion mass problem, and a desire to preserve the accidental symmetries of the Standard Model (SM), we extend the SM by an anomalous $U(1)X$ gauge symmetry where $X=Y3+a(L\mu -L\tau )/6$. The heavy $Z\prime$ boson associated with spontaneously breaking $U(1)X$ at the TeV scale mediates the $b\to s\ell \ell$ anomalies via $O9\mu \sim 1\Lambda 2(s¯\gamma \rho PLb)(\mu ¯\gamma \rho \mu )$. We show that this model, which features mixed gauge anomalies involving $U(1)X$ and hypercharge, can be made anomaly-free for any $a\in Z$ by integrating in a pair of charged fermions whose masses naturally reside somewhere between 1 and 30 TeV. The gauge symmetry permits only the third family Yukawas at the renormalisable level, and so the light quark masses and mixings are controlled by accidental $U(2)3$ flavour symmetries which we assume are minimally broken alongside $U(1)X$. The lepton sector is not governed by $U(2)$ symmetries, but rather one expects a nearly diagonal charged lepton Yukawa with $me,\mu \ll m\tau$. The model does not explain the hierarchy $me\ll m\mu$, but it does possess high quality lepton flavour symmetries that are robust to the heavy physics responsible for generating $me,\mu$. We establish the viability of these models by checking agreement with the most important experimental constraints. We comment on how the model could also explain neutrino masses and the muon $g-2$.