Encourage natural predators, like cats, but otherwise traps should be the most effective measure. The old fashioned spring mouse traps are perhaps the best and can be laid down around the affected area. Like with any pest, you have to persevere and there is no 'quick fix' to suddenly eliminate a whole population.
Using poison, you are quite likely to poison pets and other wild life which does no harm in the garden.

I tried several things without success, and finally sprinkled chilli pepper round the shrubs they were eating . No more trouble since then!