During replication-coupled DNA interstrand crosslink (ICL) repair, the XPF-ERCC1 endonuclease is required for the incisions that release, or “unhook”, ICLs, but the mechanism of ICL unhooking remains largely unknown. Incisions are triggered when the nascent leading strand of a replication fork strikes the ICL. Here, we report that while purified XPF-ERCC1 incises simple ICL-containing model replication fork structures, the presence of a nascent leading strand, modelling the effects of replication arrest, inhibits this activity. Strikingly, the addition of the single-stranded DNA (ssDNA)-binding replication protein A (RPA) selectively restores XPF-ERCC1 endonuclease activity on this structure. The 5′–3′ exonuclease SNM1A can load from the XPF-ERCC1-RPA-induced incisions and digest past the crosslink to quantitatively complete the unhooking reaction. We postulate that these collaborative activities of XPF-ERCC1, RPA and SNM1A might explain how ICL unhooking is achieved in vivo.