In reply to Run_Ross_Run:
Quickest walk up to Scafell is from Wasdale - but it's a bastard to drive to from anywhere except Wasdale. As Andy says you've got the camping at the Inn, but be warned you park on the village green and carry your stuff (over a stile?) into the small campground. Not sure about facilities...can't think there are hot showers or anything. A better bet in Wasdale might be the NT campsite - not been but assume it's pleasant but a bit expensive and rather too organised.
If you'd rather do the longer walk and shorter drive from/to Borrowdale, the campsite at Stonethwaite is lovely, by the river (midges) in a wonderful setting and a mile or two down the road/path from the start of the walk at Seathwaite. Facilities are basic, doubt the showers are hot. There is camping at Seathwaite, the start of the walk, no idea about facilities.
NT campsite at Langdale is dead easy to drive to, good quality campsite (expensive, too organised, barrier = no late arrival, etc), but that's a fair old trek to Scafell (Pike). Lots of people do it though, great if you want a really big day on the hill.
Eskdale has a number of good campsites with good facilities, quite a drive but not as far as Wasdale, and definitely the most beautiful approach to Scafell. A wonderful days walking from a beautiful, quiet valley. This would probably be my favourite option.