The Research Councils have created central web-hubs with all the key data on success rates in addition to other useful data on funded grants and overall budgets.
The ESRC seems to have one of the lowest success rates. In the Nov/Dec 2010 round of their responsive mode grants there was only an 8% success rate.
The success rates for NERC varied by the scheme, in the last round of the Consortium grants only 1 was funded. If your research falls within the remit of NERC and you are within 3 years of your first academic post I would encourage you to consider putting together an application for the new investigator scheme as this had the highest success rate of 23% in the last round. Unfortunately their small grants scheme is about to be withdrawn after the September 2011 deadline.
For the AHRC the schemes with the highest success rates were the fellowship schemes and the research networking scheme. The success rates were 40% and 50% for the fellowships and early career fellowships, and 48% for the research networking in 2010-11.
If you would like guidance on which funder and scheme to apply to then our internal peer review service can provide this along with feedback on your application.