We report on an electron spin resonance study of atomic hydrogen stabilized in a solid Ne matrices carried out at a high field of 4.6 T and temperatures below 1 K. The films of Ne, slowly deposited on the substrate at the temperature ∼1 K, exhibited a high degree of porosity. We found that H atoms may be trapped in two different substitutional positions in the Ne lattice as well as inside clusters of pure molecular H2 in the pores of the Ne film. The latter type of atoms was very unstable against recombination at temperatures 0.3-0.6 K. Based on the observed nearly instant decays after rapid small increase of temperature, we evaluate the lower limit of the recombination rate constant kr ≥ 5 · 10 −20 cm 3 s −1 at 0.6 K, five orders of magnitude larger than that previously found in the thin films of pure H2 at the same temperature. Such behavior assumes a very high mobility of atoms and may indicate a solid-to-liquid transition for H2 clusters of certain sizes, similar to that observed in experiments with H2 clusters inside helium droplets (Phys. Rev. Lett 101, 205301 (2008)). We found that the efficiency of dissociation of H2 in neon films is enhanced by 2 orders of magnitude compared to that in pure H2, which is instigated by a strong emission of secondary electrons.