Guessing this might not be for a family, but depending on how wild campingy you are, I understand that there is limited camping allowed in Shining Cliff woods near Ambergate, before you get to Matlock on the A6 (from the south). It is run by Grith Pioneers who are some kind of wacky old charity. You have to sort it out through them in advance. No facilities as far as I know, just a very nice woods. I think they charge something like 50p per person. Can't find the phone number online, but found some email addresses: jill.mike1@btinternet.com or helen@twitchen.co.uk.
Oh and I'm not sure, but I imagine you'd be parking about a mile or so from where you can camp.
Joe