Complex anion structures ((AlF4)(-), (AlF5)(2-) and (AlF6)(3-)) coexist in liquid mixtures of aluminium trifluoride and alkali fluorides in composition-dependent relative concentrations and are known to interact with the alkali counterions. We present a comparative study of the static and vibrational structures of MAlF4 molecules (with M = any alkali), with the aim of developing and testing a refined model of the ionic interactions for applications to the M-Al fluoride mixtures. We find that, whereas an edge-bridged coordination is strongly favoured for Li in LiAlF4, edge-bridging and face-bridging of the alkali ion become energetically equivalent as one moves from Na to the heavier alkalis. This result is sensitive to the inclusion of alkali polarizability and may be interpreted as implying (for M = K, Rb or Cs) almost free relative rotations of the M+ and (AlF4)(-) partners at temperatures of relevance to experiment. The consistency of such a viewpoint with electron diffraction data on vapours and with Raman spectra on melts is discussed.