  We construct the first exact statistically homogeneous and isotropic
cosmological solution in which inhomogeneity has a significant effect on the
expansion rate. The universe is modelled as a Swiss Cheese, with dust FRW
background and inhomogeneous holes. We show that if the holes are described by
the quasispherical Szekeres solution, their average expansion rate is close to
the background under certain rather general conditions. We specialise to
spherically symmetric holes and violate one of these conditions. As a result,
the average expansion rate at late times grows relative to the background, i.e.
backreaction is significant. The holes fit smoothly into the background, but
are larger on the inside than a corresponding background domain: we call them
Tardis regions. We study light propagation, find the effective equations of
state and consider the relation of the spatially averaged expansion rate to the
redshift and the angular diameter distance.
