There exists a wide range of research which identifies the link between vehicle speed and accident risk. This answer identifies the key papers.
The Transport Research Laboratory conducted two reviews of 20 mph zones in 1996 and in 1998.
Both reports showed that 20 mph zones with traffic calming achieved an average 9 mph reduction in vehicle speeds and a 60 per cent. reduction in accidents whereas in those areas where there was little or no traffic calming, reductions in vehicle speeds were minimal.
For speed restrictions more generally, the Transport Research Laboratory published a review of non-UK studies in 1994 which established a link between vehicle speed and the risk of accidents. This indicated that, in broad terms, a 1 mph reduction in average speed can reduce accident risk by around 5 per cent.
In 2000 the Transport Research Laboratory published a report investigating whether this general rule could be applied to different types of UK roads and to further understand the relationship between vehicle speed and accident frequency.
The report concluded that for each 1 mph reduction in average speed the percentage reduction in accident frequency is between 2 and 7 per cent. depending on vehicle speeds and the nature and layout of the road.