In this paper, we derive the fundamental properties of 1SWASPJ011351.29+314909.7 (J0113+31), a metal-poor (-0.40 +/- 0.04 dex), eclipsing binary in an eccentric orbit (~0.3) with an orbital period of ~14.277 d. Eclipsing M dwarfs orbiting solar-type stars (EBLMs), like J0113+31, have been identified from WASP light curves and follow-up spectroscopy in the course of the transiting planet search. We present the first binary of the EBLM sample to be fully analysed, and thus, define here the methodology. The primary component with a mass of 0.945 +/- 0.045 Msun has a large radius (1.378 +/- 0.058 Rsun) indicating that the system is quite old, ~9.5 Gyr. The M-dwarf secondary mass of 0.186 +/- 0.010 Msun and radius of 0.209 +/- 0.011 Rsun are fully consistent with stellar evolutionary models. However, from the near-infrared secondary eclipse light curve, the M dwarf is found to have an effective temperature of 3922 +/- 42 K, which is ~600 K hotter than predicted by theoretical models. We discuss different scenarios to explain this temperature discrepancy. The case of J0113+31 for which we can measure mass, radius, temperature and metallicity, highlights the importance of deriving mass, radius and temperature as a function of metallicity for M dwarfs to better understand the lowest mass stars. The EBLM Project will define the relationship between mass, radius, temperature and metallicity for M dwarfs providing important empirical constraints at the bottom of the main sequence.
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