  We report the first simultaneous and independent measurements of the K$^{-}$p
$\rightarrow \Sigma^0 \, \pi^{0}$ and K$^{-}$p $\rightarrow \Lambda \, \pi^{0}$
cross sections around 100 MeV/c kaon momentum. The kaon beam delivered by the
DA$\Phi$NE collider was exploited to detect K$^-$ absorptions on Hydrogen
atoms, populating the gas mixture of the KLOE drift chamber. The precision of
the measurements ($\sigma_{K^- p \rightarrow \Sigma^0 \pi^0} = 42.8 \pm 1.5
(stat.) ^{+2.4}_{-2.0}(syst.) \ \mathrm{mb}$ and $\sigma_{K^- p \rightarrow
\Lambda \pi^0} = 31.0 \pm 0.5 (stat.) ^{+1.2}_{-1.2}(syst.) \ \mathrm{mb}\,$)
is the highest yet obtained in the low kaon momentum regime.
