  Dark matter annihilation or decay could have a significant impact on the
ionisation and thermal history of the universe. In this paper, we study the
potential contribution of dark matter annihilation (s-wave- or
p-wave-dominated) or decay to cosmic reionisation, via the production of
electrons, positrons and photons. We map out the possible perturbations to the
ionisation and thermal histories of the universe due to dark matter processes,
over a broad range of velocity-averaged annihilation cross-sections/decay
lifetimes and dark matter masses. We have employed recent numerical studies of
the efficiency with which annihilation/decay products induce heating and
ionization in the intergalactic medium, and in this work extended them down to
a redshift of $1+z = 4$ for two different reionisation scenarios. We also
improve on earlier studies by using the results of detailed structure formation
models of dark matter haloes and subhaloes that are consistent with up-to-date
$N$-body simulations, with estimates on the uncertainties that originate from
the smallest scales. We find that for dark matter models that are consistent
with experimental constraints, a contribution of more than 10% to the
ionisation fraction at reionisation is disallowed for all annihilation
scenarios. Such a contribution is possible only for decays into
electron/positron pairs, for light dark matter with mass $m_\chi \lesssim $ 100
MeV, and a decay lifetime $\tau_\chi \sim 10^{24} - 10^{25}$ s.
