  We study the propagation of ultra-high-energy cosmic rays in the magnetised
cosmic web. We focus on the particular case of highly magnetised voids ($B \sim
\text{nG}$), using the upper bounds from the Planck satellite. The cosmic web
was obtained from purely magnetohydrodynamical cosmological simulations of
structure formation considering different power spectra for the seed magnetic
field in order to account for theoretical uncertainties. We investigate the
impact of these uncertainties on the propagation of cosmic rays, showing that
they can affect the measured spectrum and composition by up to $\simeq 80\%$
and $\simeq 5\%$, respectivelly. In our scenarios, even if magnetic fields in
voids are strong, deflections of 50 EeV protons from sources closer than
$\sim\;$50 Mpc are less than $15^\circ$ in approximately 10-50% of the sky,
depending on the distribution of sources and magnetic power spectrum.
Therefore, UHECR astronomy might be possible in a significant portion of the
sky depending on the primordial magnetic power spectrum, provided that protons
constitute a sizeable fraction of the observed UHECR flux.
