We study the influence of the accumulation layer on the spectral properties of semiconducting nanowires fully covered by a superconducting shell within the framework of the Bogoliubov - de Gennes equations. It is shown that both the decrease in the thickness of the layer and the increase in the ratio of Fermi velocities in the shell and the core result in the enhancement of the spectral gap and limit the parameter range corresponding to topologically nontrivial phase. The presence of the accumulation layer can also lead to reentrant magnetic flux dependencies of the gap, which can be experimentally observed in measurements of charge transport through the nanowire in the Coulomb blockade conditions.