and CMFV models, we demonstrate that these tensions can be removed in 331 models based on the gauge group SU(3) C × SU(3) L × U(1) X both for M Z in the LHC reach and well beyond it. But the implied new physics (NP) patterns in ∆F = 1 observables depend sensitively on the value of |V cb |. Concentrating the analysis on three 331 models that have been selected by us previously on the basis of their performance in electroweak precision tests and ε /ε we illustrate this for |V cb | = 0.042 and |V cb | = 0.040. We find that these new lattice data still allow for positive shifts in ε /ε up to 6 × 10 −4 for M Z = 3 TeV and |V ub | = 0.0036 for both values of |V cb | but for M Z = 10 TeV only for |V cb | = 0.040 such shifts can be obtained. For |V ub | = 0.0042 maximal shifts in ε /ε increase to 7×10 −4 . NP effects in B s → µ + µ − and in the Wilson coefficient C 9 are significantly larger in all three models for the case of |V cb | = 0.040. In particular in two models the rate for B s → µ + µ − can be reduced by NP by 20% for M Z = 3 TeV resulting in values in the ballpark of central values from CMS and LHCb. In the third model a shift in C 9 up to C NP 9 = −0.5 is possible. For |V cb | = 0.042, NP effects in B s → µ + µ − and in C 9 are by at least a factor of two smaller. For M Z = 10 TeV NP effects in B s → µ + µ − and C 9 , independently of |V cb |, are at most at the level of a few percent. We also consider the simplest 331 model, analyzed recently in the literature, in which X = Y , the usual hypercharge. We find that JHEP08 (2016)115 in this model NP effects in flavour observables are much smaller than in the three models with X = Y , in particular NP contributions to the ratio ε /ε are very strongly suppressed. Our analysis exhibits the important role of lattice QCD and of precise values of CKM parameters, in particular |V cb |, for quark flavour phenomenology beyond the SM. It also demonstrates exceptional role of ∆F = 2 observables and of ε /ε in testing high energy scales beyond the LHC.