Nematodes are important parasites of people and animals, and in natural ecosystems they are a major ecological force. Strongyloides ratti is a common parasitic nematode of wild rats and we have investigated its population genetics using single-worm, whole-genome sequencing. We find that S. ratti populations in the UK consist of mixtures of mainly asexual lineages that are widely dispersed across a host population. These parasite lineages are likely very old and may have originated in Asia from where rats originated. Genes that underly the parasitic phase of the parasite's life cycle are hyperdiverse compared with the rest of the genome, and this may allow the parasites to maximise their fitness in a diverse host population. These patterns of parasitic nematode population genetics have not been found before and may also apply to Strongyloides spp. that infect people, which will affect how we should approach their control.