The site you saw in Bradwell was probably Eden Tree House. I'm fairly certain that this is for tourers only but you could try phoning to check:
Eden Tree House Caravan Park
Eccles Lane, Bradwell, Hope Valley, Derbyshire, S33 9JT
Tel: 01433 623444
The site near Hope might be Laneside Caravan Park. This also seems to be only for tourers:
http://www.lanesidecaravanpark.co.uk/
There are some cottages to let on the Laneside site. Would these be of any interest to you?
http://www.peakdistrictholidaycottages.com/
Alternatively, if you're only looking for static caravans, you could try somewhere just outside of the National Park boundary, such as Lime Tree Park, Buxton:
http://www.limetreeparkbuxton.co.uk/
There are also 3 statics for hire at Longnor Wood, which is an 'adults only' site at the northern end of Dovedale, close to both Buxton and Bakewell:
http://www.longnorwood.co.uk
Chris