Genomic prediction utilizes single nucleotide polymorphism (SNP) chip data to predict animal genetic merit. It has the advantage of potentially capturing the effects of the majority of loci that contribute to genetic variation in a trait, even when the effects of the individual loci are very small. To implement genomic prediction, marker effects are estimated with a training set, including individuals with marker genotypes and trait phenotypes; subsequently, genomic estimated breeding values (GEBV) for any genotyped individual in the population can be calculated using the estimated marker effects. In this study, we aimed to: (i) evaluate the potential of genomic prediction to predict GEBV for nematode resistance traits and BW in sheep, within and across populations; (ii) evaluate the accuracy of these predictions through within-population cross-validation; and (iii) explore the impact of population structure on the accuracy of prediction. Four data sets comprising 752 lambs from a Scottish Blackface population, 2371 from a Sarda × Lacaune backcross population, 1000 from a Martinik Black-Belly × Romane backcross population and 64 from a British Texel population were used in this study. Traits available for the analysis were faecal egg count for Nematodirus and Strongyles and BW at different ages or as average effect, depending on the population. Moreover, immunoglobulin A was also available for the Scottish Blackface population. Results show that GEBV had moderate to good within-population predictive accuracy, whereas across-population predictions had accuracies close to zero. This can be explained by our finding that in most cases the accuracy estimates were mostly because of additive genetic relatedness between animals, rather than linkage disequilibrium between SNP and quantitative trait loci. Therefore, our results suggest that genomic prediction for nematode resistance and BW may be of value in closely related animals, but that with the current SNP chip genomic predictions are unlikely to work across breeds.