I'm not at all well-versed in campsites but for our first foray, we went here - White Mark Farm. It's in Watlington. Depends whereabouts you are in Berks, but if you were Reading-ish, then it would take you only about 40 mins to drive there (assuming you don't leave during the horrible Reading rush-hour!). It is a lovely little campsite - basic but comfortable. Free hot showers, lovely clean shower block, nice covered kitchen with plenty of sinks, and a microwave and kettle, plus sockets for recharging things. A couple of flat, glassy fields with nice plantings making it feel less flat and square. And views all around of the Chilterns. Lots of Red Kites. Friendly owner. Think it cost us £13 for a tent, two adults and two children.