Mutations in, and the altered expression of, epigenetic modifiers are pervasive in human tumours, making epigenetic factors attractive antitumour targets. The open-versus-closed chromatin state within the cells-of-origin of cancer correlates with the uneven distribution of mutations. However, the long-term effect of targeting epigenetic modifiers on mutability in patients with cancer is unclear. Here, we increased chromatin accessibility by deleting the histone H3 lysine 9 (H3K9) methyltransferase G9a in murine epidermis and show that this does not alter the single nucleotide variant burden or global genomic distribution in chemical mutagen-induced squamous tumours. G9a-depleted tumours develop after a prolonged latency compared with their wild-type counterparts, but are more aggressive and have an expanded cancer progenitor pool, pronounced genomic instability and frequent loss-of-function p53 mutations. Thus, we call for caution when assessing long-term therapeutic benefits of chromatin modifier inhibitors, which may promote more aggressive disease.