Plume magmatism and continental breakup led to the opening of the northeast Atlantic Ocean during the globally warm early Cenozoic. This warmth culminated in a transient (170 thousand year, kyr) hyperthermal event associated with a large, if poorly constrained, emission of carbon called the Palaeocene–Eocene Thermal Maximum (PETM) 56 million years ago (Ma). Methane from hydrothermal vents in the coeval North Atlantic Igneous Province (NAIP) has been proposed as the trigger, though isotopic constraints from deep sea sediments have instead implicated direct volcanic carbon dioxide (CO2) emissions. Here we calculate that background levels of volcanic outgassing from mid-ocean ridges and large igneous provinces yield only one-fifth of the carbon required to trigger the hyperthermal. However, geochemical analyses of volcanic sequences spanning the rift-to-drift phase of the NAIP indicate a sudden ~220 kyr-long intensification of magmatic activity coincident with the PETM. This was likely driven by thinning and enhanced decompression melting of the sub-continental lithospheric mantle, which critically contained a high proportion of carbon-rich metasomatic carbonates. Melting models and coupled tectonic–geochemical simulations indicate that >104 gigatons of subcrustal carbon was mobilized into the ocean and atmosphere sufficiently rapidly to explain the scale and pace of the PETM.