  Neutral Hydrogen Intensity Mapping (HI IM) surveys will be a powerful new
probe of cosmology. However, strong astrophysical foregrounds contaminate the
signal and their coupling with instrumental systematics further increases the
data cleaning complexity. In this work, we simulate a realistic single-dish HI
IM survey of a $5000$~deg$^2$ patch in the $950 - 1400$ MHz range, with both
the MID telescope of the SKA Observatory (SKAO) and MeerKAT, its precursor. We
include a state-of-the-art HI simulations and explore different foreground
models and instrumental effects such as non-homogeneous thermal noise and beam
side-lobes. We perform the first Blind Foreground Subtraction Challenge for HI
IM on these synthetic data-cubes, aiming to characterise the performance of
available foreground cleaning methods with no prior knowledge of the sky
components and noise level. Nine foreground cleaning pipelines joined the
Challenge, based on statistical source separation algorithms, blind polynomial
fitting, and an astrophysical-informed parametric fit to foregrounds. We devise
metrics to compare the pipeline performances quantitatively. In general, they
can recover the input maps' 2-point statistics within 20 per cent in the range
of scales least affected by the telescope beam. However, spurious artefacts
appear in the cleaned maps due to interactions between the foreground structure
and the beam side-lobes. We conclude that it is fundamental to develop accurate
beam deconvolution algorithms and test data post-processing steps carefully
before cleaning. This study was performed as part of SKAO preparatory work by
the HI IM Focus Group of the SKA Cosmology Science Working Group.
