There is limited accommodation in the village on Newnham itself - but there is a variety in the surrounding area. If searching by distance, try to ensure your accommodation is west of the river Severn - places 5 miles away on a map can be an hour's drive.
Nearby Littledean has two hotels
Set in the centre of the forest, The Speech House is pleasant. But not cheap.
There are a few bed and breakfasts nearby, and no doubt more if you go further into the forest.
There are numerous other holiday cottages in the area...
Further accommodation options can be found here.
