  A late end to reionisation at redshift $z\simeq 5.3$ is consistent with
observed spatial variations in the Ly$\alpha$ forest transmission and the
deficit of Ly$\alpha$ emitting galaxies around extended Ly$\alpha$ absorption
troughs at $z=5.5$. In this model, large islands of neutral hydrogen should
persist in the diffuse intergalactic medium (IGM) until $z\simeq 6$. We use a
novel, hybrid approach that combines high resolution cosmological
hydrodynamical simulations with radiative transfer to predict the incidence of
strong 21 cm forest absorbers with optical depths $\tau_{21}>10^{-2}$ from the
diffuse IGM in these late reionisation models. We include the effect of
redshift space distortions on the simulated 21 cm forest spectra, and treat the
highly uncertain heating of the pre-reionisation IGM by soft X-rays as a free
parameter. For a model with only modest IGM pre-heating, such that average gas
kinetic temperatures in the diffuse IGM remain below $T_{\rm K}\simeq 10^{2}
\rm\, K$, we find that strong 21 cm forest absorption lines should persist
until $z=6$. For a sample of $\sim 10$ sufficiently radio loud background
sources, a null-detection of 21 cm forest absorbers at $z\simeq 6$ with
SKA1-low or possibly LOFAR should provide an informative lower limit on the
still largely unconstrained soft X-ray background at high redshift and the
temperature of the pre-reionisation IGM.
