The potential germline effects of radiation exposure to military veterans present at British nuclear tests in Australia and the South Pacific is of considerable interest. We analyzed germline mutations in 60 families of UK military personnel comprising 30 control and 30 nuclear test veterans (NTV). Using whole-genome sequencing we studied the frequency and spectra of de novo mutations to investigate the transgenerational effect of veterans' (potential) exposure to radiation at nuclear bomb test sites. We find no elevation in total de novo single nucleotide variants, small insertion-deletions, structural variants or clustered mutations among the offspring of nuclear test veterans compared to those of control personnel. We did observe an elevated occurrence of single base substitution mutations within mutation signature SBS16, due to a subset of NTV offspring. The relevance of this elevation to potential exposure of veteran fathers and, future health risks, require further investigation. Overall, we find no evidence of increased mutations in the germline of a group of British nuclear test veterans. ISRCTN Registry 17461668.