hi
camping is not normally allowed in the country unless in a proper campsite. there are however loads in the peaks and only charge about £4 a head. if ur struggling to find places i can help out. many are shown on OS maps of the area.
in 'open accesses land' (
http://www.openaccess.gov.uk/) areas, although camping is not allowed, is generally acceptable to 'wild' camp as long as no mess, noise is made and that ur out of site is between 5pm and 8am ish.
as MILF-Hunter said trains and buses are fine-may take some time, but u'll get there. only issue is getting about once your there. but, having said that, u can plan for it and chose an area to camp and walk need train station. buxton, matlock, castleton, bake well are the more major towns i'd suggest investigating.
u'd have 2 check with the dvla for car rental and licensing rules.
http://www.dvla.gov.uk/ hope this helps!