Histone-modifying systems play fundamental roles in gene regulation and the development of multicellular organisms. Histone modifications that are enriched at gene regulatory elements have been heavily studied, but the function of modifications that are found more broadly throughout the genome remains poorly understood. This is exemplified by histone H2A mono-ubiquitylation (H2AK119ub1) which is enriched at Polycomb-repressed gene promoters, but also covers the genome at lower levels. Here, using inducible genetic perturbations and quantitative genomics, we discover that the BAP1 deubiquitylase plays an essential role in constraining H2AK119ub1 throughout the genome. Removal of BAP1 leads to pervasive accumulation of H2AK119ub1, which causes widespread reductions in gene expression. We show that elevated H2AK119ub1 represses gene expression by counteracting transcription initiation from gene regulatory elements, causing reductions in transcription-associated histone modifications. Furthermore, failure to constrain pervasive H2AK119ub1 compromises Polycomb complex occupancy at a subset of Polycomb target genes leading to their derepression, therefore explaining the original genetic characterisation of BAP1 as a Polycomb group gene. Together, these observations reveal that the transcriptional potential of the genome can be modulated by regulating the levels of a pervasive histone modification, without the need for elaborate gene-specific targeting mechanisms.