We find that the white dwarf GD 448 is a detached white dwarf/M dwarf binary with an orbital period of 2.47h. This is the shortest period known for such a binary, placing it in the centre of the `period gap' from 2 to 3h in which few cataclysmic variable stars (mass-transferring white dwarf/main-sequence star systems) are found. The cooling age of the white dwarf (5x10^7 yr) shows that GD 448 was born in the gap and has never been a cataclysmic variable star. We measure radial velocity semi-amplitudes of K_W=31.2+/-1.5 km s^-1 and K_E=122.2+/-1.1 km s^-1 from Hα absorption from the white dwarf and Hα and CaII triplet emission from the M star. The white dwarf absorption shows a gravitational redshift of 16.8+/-1.6 km s^-1, leading to a mass of 0.44+/-0.03 M_solar for the white dwarf. The Hα and CaII emission-line fluxes are modulated by a factor of 4, and are strongest when the M dwarf is furthest from us. The flux variation is consistent with emission proportional to the irradiating flux from the white dwarf, and yet the latter is not hot enough to have produced the emission by photoionization alone. The asymmetric distribution means that K_E is less than the true K velocity of the M star, K_M. From models of the emission we find that 138<K_M<168 km s^-1 and 0.08<M_M<0.10 M_solar. Our models independently predict light curves close to those observed. If the M dwarf is close to its main-sequence radius, GD 448 will begin to transfer mass when its orbital period is ~=1h. A great surprise is that the width of the Hα emission from the M dwarf can only be matched with the addition of 90 km s^-1 FWHM broadening. The excess broadening does not affect the CaII emission, and this suggests that it may arise from thermal or pressure broadening.