  We investigate the energy dependence of the photo-production cross-section of
vector mesons $J/\Psi$ and $\Upsilon$, measured by both HERA experiments H1 and
ZEUS in electron-proton collisions and by LHC experiments ALICE, CMS and LHCb
in ultra-peripheral proton-proton and ultra-peripheral proton-lead collisions.
Our study uses 2 particular fits of inclusive unintegrated gluon distribution,
based on non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and
next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution
(Hentschinski-Sabio Vera-Salas gluon; HSS). We find that linear next-to-leading
order BFKL evolution can only describe production at highest energies, if
perturbative corrections are increased to unnaturally large values; rendering
this corrections small, the growth with energy is too strong in the LHC region
and the description of $J/\Psi$ data fails. For the KS gluon we find that an
accurate description of $J/\Psi$ data is possible if non-linear corrections to
low x QCD evolution are taken into account; without such correction a
description of data fails. We interpret this observation as a clear signal for
the presence of high gluon densities in low x the proton, characteristic for
the onset of gluon saturation.
