Although observations of recent volcanic eruptions beneath Vatnajokull, Iceland have improved the understanding of ice deformation and meltwater drainage, little is known about the processes that occur at the glacier base. We present observations of the products of a small-volume, effusive subglacial rhyolite eruption at Blahnukur, Torfajokull, Iceland. Lava bodies, typically 7 m long, have unusual conical morphologies and columnar joint orientations that suggest emplacement within cavities melted into the base of a glacier. Cavities appear to have been steep-walled and randomly distributed. These features can be explained by a simple model of conductive heat loss during the ascent of a lava body to the glacier base. The released heat melts a cavity in the overlying ice. The development of vapour-escape pipes in the waterlogged, permeable breccias surrounding the lava allows rapid heat transfer between lava and ice. The formed meltwater percolates into the breccias, recharging the cooling system and leaving a steam-filled cavity. The slow ascent rates of intrusive rhyolitic magma bodies provide ample time for a cavity to be melted in the ice above, even during the final 10 m of ascent to the glacier base. An equilibrium cavity size is calculated at which melting is balanced by creep closure. This is dependent upon the heat input and the difference between glaciostatic and cavity pressure. The cavity sizes inferred from Blahnukur are consistent with a pressure differential of 2-4 MPa, suggesting that the ice was at least 200 m thick. This is consistent with the volcanic stratigraphy, which indicates that the ice exceeded 350 m in thickness. Although this is the first time that a subglacial cavity system of this type has been reconstructed from an ancient volcanic sequence, it shares many characteristics with the modern firn cave system formed by fumarolic melting within the summit crater of Mount Rainier, Washington. At both localities, it appears that localised heating at the glacier base has resulted in heterogeneous melting patterns. Despite the different rheological properties of ice and firn, similar patterns of cavity roof deformation are inferred. The development of low-pressure subglacial cavities in regions of high heat flux may influence the trajectory of rising magma, with manifold implications for eruptive mechanisms and resultant subglacial volcanic landforms.