  We study an extension of the Standard Model that addresses the hints of
lepton flavour universality violation observed in $B\to K^{(*)} l^+l^-$ decays
at LHCb, while providing a viable candidate for dark matter. The model
incorporates two new scalar fields and a Majorana fermion that induce one-loop
contributions to $B$ meson decays. We show that agreement with observational
data requires the new couplings to be complex and that the Majorana fermion can
reproduce the observed dark matter relic density. This combination of
cosmological and flavour constraints sets an upper limit on the dark matter and
mediator masses. We have studied LHC dijet and dilepton searches, finding that
they rule out large regions of parameter space by setting lower bounds on the
dark matter and mediator masses. In particular, dilepton bounds are much more
constraining in a future high-luminosity phase. Finally, we have computed the
scattering cross section of dark matter off nuclei and compared it to the
sensitivity of current and future direct detection experiments, showing that
parts of the parameter space could be accessible in the future to multi-ton
experiments. Future collider and direct DM searches complement each other to
probe large areas of the parameter space of this model.
