  We reconsider the inclusive production of isolated prompt photons in $pp$
collisions at the LHC energies in the framework of $k_T$-factorization
approach. Our analysis is based on the ${\cal O}(\alpha \alpha_s)$ off-shell
(depending on the transverse momenta of initial quarks and gluons) production
amplitudes of $q^* g^* \to \gamma q$ and $q^* \bar q^* \to \gamma g$ partonic
subprocesses and transverse momentum dependent (or unintegrated) quark and
gluon densities in a proton, which are chosen in accordance with the
Kimber-Martin-Ryskin prescription. We show that the sub-leading high-order
${\cal O}(\alpha \alpha_s^2)$ contributions, not covered by the non-collinear
evolution of parton densities, are important to describe latest LHC data.
