If you get some weld mesh, you can put this under and a compost bin, this would stop rats but not mice.
Rats will chew through plastic and wood, so store everything in metal bins.
Runs should be L shaped under the soil by at least a spade depth and width to keep rats out.
You could put rat traps down, making sure that other creatures are safe from this.
Homebase sells weld mesh at a good price.