Campsites are now, thanks to loads of new laws, geared up more than ever for an enjoyable experience.

If you want mountains you have The Lake District, Yorkshire Dales, Derbyshire, Wales and even places like Exmoor and Dartmoor in the South West.
Further afield you have Scotland with many sites and wonderful places to chose from.
Some of these sites are owned either by the Camping / Caravan Club of Great Britain or The National Trust.

In the Lake District we stayed at the Nat Trust camp site at Wasdale, on the edge of Wastwater and looking directly onto Scafel Pike and The Great Gable. I still maintain this is the nearest to heaven I'll get on earth ! There's a Pub / Hotel about one mile away, but the nearest shop is 3 miles along a narrow windy road. It's completely out of range of all signals, so no mobiles going off half the day and night etc.
I cannot recommend this site more highly.

In North Wales we stayed at a site on the slopes of Tryfan, a majestic mountain peak offering many routes and other walks around and about.
Again, being remote, this does not attract many people other than climbers, walkers and back packers - ideal. By the end of a day walking in places such as these, you want to go to bed early when you get back !

Maybe I've sounded a bit of a grumpy old man in saying a lot about avoiding noise and kids.
If you want that, most seaside resorts have excellant campsites with all amenities and catering for just about everyone.
Some 'Holiday Camps' now have campsite areas and this can be looked into.

Your holiday is usually as good as the campsite you're staying at so I re-iterate the importance of researching thoroughly before you decide.

Look at the places which are not the known popular places. Some areas have that 'not a holiday place' ring about them. These are the places where you may find the perfect place and setting.