  This paper presents 52 X-ray bright galaxy clusters selected within the 11
deg$^2$ XMM-LSS survey. 51 of them have spectroscopic redshifts
($0.05<z<1.06$), one is identified at $z_{\rm phot}=1.9$, and all together make
the high-purity "Class 1" (C1) cluster sample of the XMM-LSS, the highest
density sample of X-ray selected clusters with a monitored selection function.
Their X-ray fluxes, averaged gas temperatures (median $T_X=2$ keV),
luminosities (median $L_{X,500}=5\times10^{43}$ ergs/s) and total mass
estimates (median $5\times10^{13} h^{-1} M_{\odot}$) are measured, adapting to
the specific signal-to-noise regime of XMM-LSS observations. The redshift
distribution of clusters shows a deficit of sources when compared to the
cosmological expectations, regardless of whether WMAP-9 or Planck-2013 CMB
parameters are assumed. This lack of sources is particularly noticeable at $0.4
\lesssim z \lesssim 0.9$. However, after quantifying uncertainties due to small
number statistics and sample variance we are not able to put firm (i.e. $>3
\sigma$) constraints on the presence of a large void in the cluster
distribution. We work out alternative hypotheses and demonstrate that a
negative redshift evolution in the normalization of the $L_{X}-T_X$ relation
(with respect to a self-similar evolution) is a plausible explanation for the
observed deficit. We confirm this evolutionary trend by directly studying how
C1 clusters populate the $L_{X}-T_X-z$ space, properly accounting for selection
biases. We point out that a systematically evolving, unresolved, central
component in clusters and groups (AGN contamination or cool core) can impact
the classification as extended sources and be partly responsible for the
observed redshift distribution.[abridged]
