We present an analysis of the X-ray properties of the Magellanic-type galaxy NGC 55 based on two contiguous XMM-Newton observations. We detect a total of 137 X-ray sources in the field of view, 42 of which are located within the optical confines of the galaxy. On the basis of X-ray colour classification and after correcting for background objects, we conclude that our source sample includes ~ 20 X-ray binaries, 5 supernova remnants and 7 very soft sources (including 2 good candidate supersoft sources) associated with NGC 55. Detailed spectral and timing analysis was carried out on 4 of the brightest X-ray sources. One of these objects is identified with a Galactic foreground star and is a possible new RS CVn system. The other three are consistent with accreting X-ray binaries, though further evidence of short term variability is required to confirm this. We also find evidence of an underlying component, which is concentrated on the bar region but has an extent of at least 6' (3 kpc) in the plane of the galaxy and +/- 1' (+/- 500 pc) perpendicular to it. This emission is best fitted by a thermal plasma plus power-law model but with high intrinsic absorption consistent with its location in the central disc of the galaxy. We interpret the soft component as diffuse thermal emission linked to regions of current star formation, whilst the hard power-law component may originate in unresolved X-ray binary sources. The intrinsic luminosity of this residual disc emission may exceed Lx ~ 6e38 ergs/s (0.3-6 keV). A comparison with other Magellanic systems confirms that, in terms of both its discrete X-ray source population and its extended emission, NGC 55 has X-ray properties which are typical of its class. Comment: 17 pages, 8 figures, accepted for publication in MNRAS