The Swift Gamma Ray Burst satellite routinely provides prompt positions for GRBs and their afterglows on timescales of a few hundred seconds. However, with a pointing accuracy of only a few arcminutes, and a systematic uncertainty on the star-tracker solutions to the World Coordinate System of 3-4 arcsec, the precision of the early XRT positions is limited to 3-4 arcsec at best. This is significant because operationally, the XRT detects >95% of all GRBs, while the UVOT detects only the optically brightest bursts, ~30% of all bursts detected by BAT; thus early and accurate XRT positions are important because for the majority of bursts they provide the best available information for the initial ground-based follow-up campaigns. Here we describe an autonomous way of producing more accurate prompt XRT positions for GRBs and their afterglows, based on UVOT astrometry and a detailed mapping between the XRT and UVOT detectors. The latter significantly reduces the dominant systematic error - the star-tracker solution to the World Coordinate System. This technique, which is limited to times when there is significant overlap between UVOT and XRT PC-mode data, provides a factor of 2 improvement in the localisation of XRT refined positions on timescales of less than a few hours. Furthermore, the accuracy achieved is superior to astrometrically corrected XRT PC mode images at early times (for up to 24 h), for the majority of bursts, and is comparable to the accuracy achieved by astrometrically corrected X-ray positions based on deep XRT PC-mode imaging at later times.