Thermal radiative emission from a hot surface to a cold surface plays an important role in many applications, including energy conversion, thermal management, lithography, data storage and thermal microscopy. Recent studies on bulk materials have confirmed long-standing theoretical predictions indicating that when the gap between the surfaces is reduced to tens of nanometres, well below the peak wavelength of the blackbody emission spectrum, the radiative heat flux increases by orders of magnitude. However, despite recent attempts, whether such enhancements can be obtained in nanoscale dielectric films thinner than the penetration depth of thermal radiation, as suggested by theory, remains experimentally unknown. Here, using an experimental platform that comprises a heat-flow calorimeter with a resolution of about 100 pW (ref. 7), we experimentally demonstrate a dramatic increase in near-field radiative heat transfer, comparable to that obtained between bulk materials, even for very thin dielectric films (50-100 nm) when the spatial separation between the hot and cold surfaces is comparable to the film thickness. We explain these results by analysing the spectral characteristics and mode shapes of surface phonon polaritons, which dominate near-field radiative heat transport in polar dielectric thin films.