  We analyze the exclusive rare $B \to K^{(*)} \ell^+ \ell^-$, $B \to K^{(*)}
\nu \bar \nu$ and $B \to K^* \gamma$ decays in the Applequist-Cheng-Dobrescu
model, which is an extension of the Standard Model in presence of universal
extra dimensions. In particular, we consider the case of a single universal
extra dimension. We study how spectra, branching fractions and asymmetries
depend on the compactification parameter 1/R, and whether the hadronic
uncertainty due to the form factors obscures or not such a dependence. We find
that, using present data, it is possible in many cases to put a sensible lower
bound to 1/R, the most stringent one coming from $B \to K^* \gamma$. We also
study how improved experimental data can be used to establish stronger
constraints to this model.
