So I got to thinking about this using Long Distance Footpath routes.
Here's what I wrote, though I can't see me doing it for some time!
I live in the East Midlands so can vouch for that bit.
So you could try:
The Limestone Way (starts at Castleton - not far from Edale) to Tissington
Tissington Trail to Ashbourne
Bonnie Prince Charlie Way (Ashbourne) to west of Derby (Lees)
Derby City Nomads Circular (South) to Swarkestone
Easy footpaths from Swarkestone through Melbourne to Heath End (Staunton Harold) to pick up the Ivanhoe Way (towards Ashby).
Ivanhoe Way through to Leicestershire Round
Leicestershire Round to near Market Harborough
Link your way through to Hobblers Way
Hobblers Way to Grand Union Canal
Grand Union Canal Walk to London
Thames Down Link
North Downs Way to Canterbury
Obviously there are hundreds of variations of this route you could take.
You could do much of it by canal from Heanor Derbys to London but that could be boring for the whole length.
Also the Midshires Way from north of Derby goes a long way south and is quite well marked.
The Derwent Valley route goes roughly Sheffield to Derby.
Best starting websites: