The loss of recombination between sex chromosomes has occurred repeatedly throughout nature, with important implications for their subsequent evolution. Explanations for this remarkable convergence have generally invoked only adaptive processes (e.g. sexually antagonistic selection); however, there is still little evidence for these hypotheses. Here we propose a model in which recombination on sex chromosomes is lost due to the neutral accumulation of sequence divergence adjacent to (and thus, in linkage disequilibrium with) the sex determiner. Importantly, we include in our model the fact that sequence divergence, in any form, reduces the probability of recombination between any two sequences. Using simulations, we show that, under certain conditions, a region of suppressed recombination arises and expands outwards from the sex-determining locus, under purely neutral processes. Further, we show that the rate and pattern of recombination loss are sensitive to the pre-existing recombination landscape of the genome and to sex differences in recombination rates, with patterns consistent with evolutionary strata emerging under some conditions. We discuss the applicability of these results to natural systems. This article is part of the theme issue 'Challenging the paradigm in sex chromosome evolution: empirical and theoretical insights with a focus on vertebrates (Part I)'.