  The abnormally fast orbital decay observed in the black hole (BH) Low-Mass
X-ray binaries (BH-LMXB) A0620-00 and XTE J1118+480 can be explained by the
dynamical friction between Dark Matter (DM) and the companion star orbiting
around the low-mass BH (of a few $M_\odot$) of the system. In this case the
value of the index $\gamma_{\rm sp}$ of the DM spike surrounding the BH can be
pinned down with an accuracy of a few percent, way better than that for much
bigger systems such as the super massive BHs (SMBHs) in the Galactic Center or
in M87. We have used data from XTE J1118+480 to put bounds on the WIMP
annihilation cross section times velocity $\langle \sigma v\rangle$, assuming
that DM annihilation is driven by the $b\bar{b}$ annihilation channel and that
it proceeds in $s$-wave. The bounds are driven by the radio synchrotron signal
produced by $e^\pm$ final states propagating in the magnetic field near the BH.
For DM masses $m_\chi$ up to the TeV scale XTE J1118+480 allows to constrain
$\langle \sigma v\rangle$ well below $\langle\sigma v\rangle_{\rm thermal}$,
corresponding to the observed DM relic density in the Universe for a thermal
WIMP. On the other hand, for $m_\chi \gtrsim$ 15 GeV, the bounds from the SMBHs
in the GC or in M87 do not reach $\langle\sigma v\rangle_{\rm thermal}$ when
the very large uncertainties on the corresponding spike indices are taken into
account, in spite of potentially producing much larger DM densities compared to
XTE J1118+480. Our bounds for XTE J1118+480 have a mild sensitivity on spatial
diffusion, but diffusion enhances the sensitivity of the results upon the
intensity of the magnetic field. Taken at face value the bound from XTE
J1118+480 on $\langle \sigma v\rangle$ is the most constraining compared to all
others for $m_\chi\lesssim$ 1 TeV, unless the intensity of the magnetic field
is significantly smaller than its equipartition estimation.
