Also, you cannot ride across the Lulworth Firing Ranges. When they are shut, the army continue firing even if you are in the exclusion zone and even when they are open, bikes are banned and the Range Wardens still patrol for safety reasons so people don't stray off the paths as there is a significant unknown amount of unexploded ordnance (bombs and missiles). You can cycle the roads when the ranges are open, but not the trails.
The range walks are shown on Ordnance Survey maps: Landranger 19 (Dorchester & Weymouth) and OL15 (Purbeck & South Dorset).