Cullin 4 (Cul4)-based ubiquitin ligases emerged as critical regulators of DNA replication and repair. Over 50 Cul4-specific adaptors (DNA damage-binding 1 (Ddb1)-Cul4-associated factors; DCAFs) have been identified and are thought to assemble functionally distinct Cul4 complexes. Using a live-cell imaging-based RNAi screen, we analysed the function of DCAFs and Cul4-linked proteins, and identified specific subsets required for progression through G1 and S phase. We discovered C6orf167/Mms22-like protein (Mms22L) as a putative human orthologue of budding yeast Mms22, which, together with cullin Rtt101, regulates genome stability by promoting DNA replication through natural pause sites and damaged templates. Loss of Mms22L function in human cells results in S phase-dependent genomic instability characterised by spontaneous double-strand breaks and DNA damage checkpoint activation. Unlike yeast Mms22, human Mms22L does not stably bind to Cul4, but is degraded in a Cul4-dependent manner and upon replication stress. Mms22L physically and functionally interacts with the scaffold-like protein Nfkbil2 that co-purifies with histones, several chromatin remodelling and DNA replication/repair factors. Together, our results strongly suggest that the Mms22L-Nfkbil2 complex contributes to genome stability by regulating the chromatin state at stalled replication forks.