We present colours of sources detected with the Herschel/SPIRE instrument in deep extragalactic surveys of the Lockman Hole, Spitzer-FLS, and GOODS-N fields in three photometric bands at 250, 350 and 500 mu m. We compare these with expectations from the literature and discuss associated uncertainties and biases in the SPIRE data. We identify a 500 mu m flux limited selection of sources from the HerMES point source catalogue that appears free from neighbouring/blended sources in all three SPIRE bands. We compare the colours with redshift tracks of various contemporary models. Based on these spectral templates we show that regions corresponding to specific population types and redshifts can be identified better in colour-flux space. The redshift tracks as well as the colour-flux plots imply a majority of detected objects with redshifts at 1 < z < 3.5, somewhat depending on the group of model SEDs used. We also find that a population of sources with S-250/S-350 < 0.8 at fluxes above 50 mJy as observed by SPIRE are not well represented by contemporary models and could consist of a mix of cold and lensed galaxies.