Under enhanced greenhouse conditions, climate models suggest an increase in rainfall intensities in the northern Hemisphere. Major flood events in the UK during autumn 2000 and central Europe in August 2002, have focussed attention on the dramatic impacts these changes may have on many sectors of society. In the companion paper [Fowler et al., J. Hydrol. (2004) this issue], we suggested that the HadRM3H model may be used with some confidence to estimate extreme rainfall distributions, showing good predictive skill in estimating statistical properties of extreme rainfall during the baseline period, 1961-1990. In this study, we use results from the future integration of HadRM3H (following the IPCC SRES scenario A2 for 2070-2100) to assess possible changes in extreme rainfall across the UK using two methods: regional frequency analysis and individual grid box analysis. Results indicate that for short duration events (1-2 days), event magnitude at a given return period will increase by 10% across the UK. For longer duration events (5-10 days), event magnitudes at given return periods show large increases in Scotland (up to +30%), with greater relative change at higher return periods (25-50 years). In the rest of the UK, there are small increases in the magnitude of more frequent events (up to +10%) but reductions at higher return periods (up to -20%). These results provide information to alter design storm depths to examine climate change impacts on various structures. The uncertainty bounds of the estimated changes and a 'scaling' methodology are additionally detailed. This allows the estimation of changes for the 2020s, 2050s and 2080s, and gives some confidence in the use of these estimates in impact studies.