Promoters are DNA sequences that have an essential role in controlling gene expression. While recent whole cancer genome analyses have identified numerous hotspots of somatic point mutations within promoters, many have not yet been shown to perturb gene expression or drive cancer development. As such, positive selection alone may not adequately explain the frequency of promoter point mutations in cancer genomes. Here we show that increased mutation density at gene promoters can be linked to promoter activity and differential nucleotide excision repair (NER). By analysing 1,161 human cancer genomes across 14 cancer types, we find evidence for increased local density of somatic point mutations within the centres of DNase I-hypersensitive sites (DHSs) in gene promoters. Mutated DHSs were strongly associated with transcription initiation activity, in which active promoters but not enhancers of equal DNase I hypersensitivity were most mutated relative to their flanking regions. Notably, analysis of genome-wide maps of NER shows that NER is impaired within the DHS centre of active gene promoters, while XPC-deficient skin cancers do not show increased promoter mutation density, pinpointing differential NER as the underlying cause of these mutation hotspots. Consistent with this finding, we observe that melanomas with an ultraviolet-induced DNA damage mutation signature show greatest enrichment of promoter mutations, whereas cancers that are not highly dependent on NER, such as colon cancer, show no sign of such enrichment. Taken together, our analysis has uncovered the presence of a previously unknown mechanism linking transcription initiation and NER as a major contributor of somatic point mutation hotspots at active gene promoters in cancer genomes.