  We propose a viable minimal model with spontaneous CP violation in the
framework of a Two Higgs Doublet Model. The model is based on a generalised
Branco-Grimus-Lavoura model with a flavoured $\mathbb{Z}_2$ symmetry, under
which two of the quark families are even and the third one is odd. The
lagrangian respects CP invariance, but the vacuum has a CP violating phase,
which is able to generate a complex CKM matrix, with the rephasing invariant
strength of CP violation compatible with experiment. The question of scalar
mediated flavour changing neutral couplings is carefully studied. In particular
we point out a deep connection between the generation of a complex CKM matrix
from a vacuum phase and the appearance of scalar FCNC. The scalar sector is
presented in detail, showing that the new scalars are necessarily lighter than
1 TeV. A complete analysis of the model including the most relevant constraints
is performed, showing that it is viable and that it has definite implications
for the observation of New Physics signals in, for example, flavour changing
Higgs decays or the discovery of the new scalars at the LHC. We give special
emphasis to processes like $t\to {\rm h} c,{\rm h} u$, as well as ${\rm h}\to
bs, bd$, which are relevant for the LHC and the ILC.
