In this paper we present the best quality XMM-Newton and Suzaku data from M82 X-1 so far. We analyze the spectra of this remarkable Ultra-Luminous X-ray Source in a self-consistent manner. We have disentangled emission from the host galaxy, responsible for the soft X-ray emission (E<2.5 keV), which is successfully described by a two-temperature thermal emission from a hot plasma in multi-phase state, plus a narrow Fe line emission at 6.7 keV. This allowed us to properly study the intrinsic continuum emission from M82 X-1. The continuum of the Suzaku spectrum is curved and the high quality data of the Suzaku spectrum allowed us to significantly detect a weakly broadened Fe K-alpha emission line. The Equivalent-Width is in the range 30-80 eV and it does not depend on the model applied for the continuum. Assuming that this line is coming from the ULX via disc fluorescence, the data indicates a disc truncation at a radius of 6-20 gravitational radii. This value is comparable to or even larger than the Innermost Stable Circular Orbit of a non-spinning (Schwarzschild) black hole. Future longer observations might test this scenario.