We investigate how the 331 models, based on the gauge group SU(3) C × SU(3) L × U(1) X face new data on B s,d → μ + μ − and B d → K ∗ ( K ) μ + μ − taking into account present constraints from Δ F = 2 observables, low energy precision measurements, LEP-II and the LHC data. In these models new sources of flavour and CP violation originate dominantly through flavour violating interactions of ordinary quarks and leptons with a new heavy Z′ gauge boson. The strength of the relevant couplings is governed by four new parameters in the quark sector and the parameter β which in these models determines the charges of new heavy fermions and gauge bosons. We study the implications of these models for $ \beta ={{{\pm n}} \left/ {{\sqrt{3}}} \right.} $ with n = 1 , 2 , 3. The case $ \beta =-\sqrt{3} $ leading to Landau singularities for M Z′ ≈ 4 TeV can be ruled out when the present constraints on Z ′ couplings, in particular from LEP-II, are taken into account. For n = 1 , 2 interesting results are found for M Z′ < 4 TeV with largest NP effects for β < 0 in B d → K ∗ μ + μ − and the one sin B s,d → μ + μ − for β > 0. As $ \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) $ can reach the values −0 . 8and −0 . 4for n = 2and n = 1, respectively the B d → K ∗ μ + μ − anomalies can be softened with the size depending on Δ M s / (Δ M s ) SM and the CP-asymmetry S ψϕ . A correlation between $ \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) $ and $ \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) $ , identified for β < 0,implies for negative $ \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) $ uniquely suppression of $ \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) $ relative to its SM value which is favoured by the data. In turn also S ψϕ < $ S_{{\psi \phi}}^{\mathrm{SM}} $ is favoured with S ψϕ having dominantly opposite sign to $ S_{{\psi \phi}}^{\mathrm{SM}} $ and closer to its central experimental value. Another triple correlation is the one between $ \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) $ , $ \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) $ and $ \mathcal{B}\left( {{B_d}\to K{\mu^{+}}{\mu^{-}}} \right) $ . NP effects in $ b\to s\nu \overline{\nu} $ transitions, $ {K^{+}}\to {\pi^{+}}\nu \overline{\nu} $ and $ {K_L}\to {\pi^0}\nu \overline{\nu} $ turn out to be small. We find that the absence of B d → K * μ + μ − anomalies in the future data and confirmation of the suppression of $ \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) $ relative to its SM value would favour $ \beta ={1 \left/ {{\sqrt{3}}} \right.} $ and M Z′ ≈ 3 TeV . Assuming lepton universality, we find an upper bound $ \left| {C_9^{\mathrm{NP}}} \right| $ ≤ 1 . 1(1 . 4) from LEP-II data for all Z ′ models with only left-handed flavour violating couplings to quarks when NP contributions to Δ M s at the level of 10%(15%) are allowed.