  The measurement of the large scale distribution of neutral hydrogen in the
late Universe, obtained with radio telescopes through the hydrogen 21cm line
emission, has the potential to become a key cosmological probe in the upcoming
years. We explore the constraining power of 21cm intensity mapping observations
on the full set of cosmological parameters that describe the $\Lambda$CDM
model. We assume a single-dish survey for the SKA Observatory and simulate the
21cm linear power spectrum monopole and quadrupole within six redshift bins in
the range $z=0.25-3$. Forecasted constraints are computed numerically through
Markov Chain Monte Carlo techniques. We extend the sampler \texttt{CosmoMC} by
implementing the likelihood function for the 21cm power spectrum multipoles. We
assess the constraining power of the mock data set alone and combined with
Planck 2018 CMB observations. We include a discussion on the impact of
extending measurements to non-linear scales in our analysis. We find that 21cm
multipoles observations alone are enough to obtain constraints on the
cosmological parameters comparable with other probes. Combining the 21cm data
set with CMB observations results in significantly reduced errors on all the
cosmological parameters. The strongest effect is on $\Omega_ch^2$ and $H_0$,
for which the error is reduced by almost a factor four. The percentage errors
we estimate are $\sigma_{\Omega_ch^2} = 0.25\%$ and $\sigma_{H_0} = 0.16\%$, to
be compared with the Planck only results $\sigma_{\Omega_ch^2} = 0.99\%$ and
$\sigma_{H_0} = 0.79\%$. We conclude that 21cm SKAO observations will provide a
competitive cosmological probe, complementary to CMB and, thus, pivotal for
gaining statistical significance on the cosmological parameters constraints,
allowing a stress test for the current cosmological model.
