We present the cross-identification and source photometry techniques used to process Herschel SPIRE imaging taken as part of the Herschel Multi-Tiered Extragalactic Survey (HerMES). Cross-identifications are performed in map-space so as to minimize source-blending effects. We make use of a combination of linear inversion and model selection techniques to produce reliable cross-identification catalogues based on Spitzer MIPS 24-μm source positions. Testing on simulations and real Herschel observations shows that this approach gives robust results for even the faintest sources (S250 ~ 10 mJy). We apply our new technique to HerMES SPIRE observations taken as part of the science demonstration phase of Herschel. For our real SPIRE observations, we show that, for bright unconfused sources, our flux density estimates are in good agreement with those produced via more traditional point source detection methods (SUSSEXtractor) by Smith et al. When compared to the measured number density of sources in the SPIRE bands, we show that our method allows the recovery of a larger fraction of faint sources than these traditional methods. However, this completeness is heavily dependent on the relative depth of the existing 24-μm catalogues and SPIRE imaging. Using our deepest multiwavelength data set in the GOODS-N, we estimate that the use of shallow 24-μm catalogues in our other fields introduces an incompleteness at faint levels of between 20-40 per cent at 250μm.