We derive the fundamental properties of 1SWASP J011351.29+314909.7 (J0113+31), a metal-poor (-0.40+/-0.04dex), eclipsing binary in an eccentric orbit (~0.3) with an orbital period of 14.277d. Eclipsing M dwarfs that orbit solar-type stars (EBLMs), like J0113+31, have been identified from their light curves and follow-up spectroscopy in the course of the WASP transiting planet search. We present the analysis of the first binary of the EBLM sample for which masses, radii and temperatures of both components are derived. The primary component with a mass of 0.945+/-0.045M_{sun} has a large radius (1.378+/-0.058R{sun}) indicating that the system is quite old, ~9.5Gyr. The M-dwarf secondary mass of 0.186+/-0.010M{sun} and radius of 0.209+/-0.011R{sun}_ 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+/-42K, which is ~600K hotter than predicted by theoretical models. We present the WASP light curve, the optical follow-up light curves, the near-infrared light curve of the secondary eclipse, and the radial velocity measurements of J0113+31.