In common with other early-type stars, epsilon Ori (B0 Ia) shows evidence for structure in its stellar wind. Variations in optical and ultraviolet line profiles reveal the presence of large-scale structure in the inner wind. The detection of X-rays and the existence of black troughs in saturated ultraviolet lines are indicative of small-scale structure. The geometric extent of both types of structure is poorly known. In principle, large-scale structure can be detected directly from very high spatial resolution observations that resolve the stellar wind. A simpler technique is to look for the presence of additional flux compared to that expected from a smooth wind. The run of this excess flux as a function of wavelength indicates how fast structure decays in the wind. If there is variability in the excess flux, it shows us that the structure must be large-scale. Such variability is suggested by two previous 6 cm radio observations of epsilon Ori: Abbott et al. (i̧teAbbott+al80) found 1.6 +/- 0.5 mJy, while Scuderi et al. (ţeScuderi+al98) measured only 0.60 +/- 0.06 mJy. This could indicate that the large-scale structure persists beyond ~ 50 R*. To further investigate this variability, we used the Very Large Array (VLA) to monitor epsilon Ori over a 5-day period in February 1999. We supplemented our data with observations from the VLA archive. In an attempt to resolve the stellar wind, we also obtained a series of high spatial resolution observations with the Multi-Element Radio Linked Interferometer Network (MERLIN) during January-March 1999. From this combined material we find no evidence for variability and we conclude that the Abbott et al. (cȩAbbott+al80) flux determination is in error. The data do show substantial excess flux at millimetre wavelengths, compared to a smooth wind. This excess is confirmed by a submillimetre observation which we obtained with the James Clerk Maxwell Telescope (JCMT). The behaviour of epsilon Ori is therefore similar to what had been found previously for alpha Cam, delta Ori A, kappa Ori and zeta Pup. While the present data do not allow very strong constraints, they show that considerable structure must persist up to at least ~ 10 R* in the wind of epsilon Ori. The combined radio fluxes are used to derive a mass-loss rate of log dot M (Msun/yr)= -5.73 +/- 0.04. This value is in good agreement with the Halpha mass-loss rate. The good agreement between Halpha and radio mass-loss rates for hot stars in general remains puzzling, as it implies that the same amount of structure is present in very different formation regions.