ROSPA have produced a helpful fact sheet looking at a wide range of evidence on the effects of 20mph speed limits.
One of the key findings is that your risk of being killed ("fatality risk") is more than 5 times worse on a 30mph road than on a 20mph road.
There are fewer accidents and when they do happen the injuries are less severe because the speed (and energy with which the vehicle is moving) is less.
It is important to remember that however safely you drive, others do not and slower speed gives more time to react to what other people do.
Some people say, "but not everyone will obey a 20mph speed limit." This is true. But they key point is that enough people do obey them, or drive slower than they would otherwise, to make a real difference that saves lives.
The ROSPA fact sheet can be read here.