*Euston to Macclesfield is 2 hours. Easy and pleasant ride to Macc. Forest. Very nice part of the world. Campsites are not plenty but some nearby. Slightly hard(er) ride to Cat and Fiddle with a mostly freewheel into Buxton and lots more camping options. Also a very nice place to spend some time. Both on the edge of but not actually IN the Peak District.
or
London to Sheffield and then ride out to Peaks or get the Sheffield to Manchester train with stops IN the Peak District at any of Grindleford, Hathersage, Bamford, Hope, Edale (or again just outside the Peak), Chinley or New Mills. LOTS of camping options. In fact there is a nice campsite 200 yards down the road from me and lots of lovely Peak bike riding, walking, pub options here (alight at New Mills Central- the stop after Chinley) and cycle down the road a bit. Hayfield is just a bit further up the very flat Sett Valley Trail as well. Chuck me an email if you think this might fit the bill and you’d like some more info**
*not South London though.
** I do not work for the High Peak Tourist Board