  The annihilation of dark matter particles is expected to yield a broad
radiation spectrum via the production of Standard Model particles in
astrophysical environments. In particular, electrons and positrons from dark
matter annihilation produce synchrotron radiation in the presence of magnetic
fields. Galaxy clusters are the most massive collapsed structures in the
universe, and are known to host $\sim\mu$G-scale magnetic fields. They are
therefore ideal targets to search for, or to constrain the synchrotron signal
from dark matter annihilation. In this work we use the expected sensitivities
of several planned surveys from the next generation of radio telescopes to
predict the constraints on dark matter annihilation models which will be
achieved in the case of non-detections of diffuse radio emission from galaxy
clusters. Specifically, we consider the Tier 1 survey planned for the Low
Frequency Array (LOFAR) at 120 MHz, the EMU survey planned for the Australian
Square Kilometre Array Pathfinder (ASKAP) at 1.4 GHz, and planned surveys for
APERTIF at 1.4 GHz. We find that, for massive clusters and dark matter masses
$\lesssim 100$ GeV, the predicted limits on the annihilation cross section
would rule out vanilla thermal relic models for even the shallow LOFAR Tier 1,
ASKAP, and APERTIF surveys.
