Unless someone particularly wanted to avoid motorways, the only sensible route from Manchester to Cambridge is via the M56, the M6 and the A14. However you won't encounter many roundabouts that way.
Using the 'avoid motorways' option on the AA Routefinder website takes you over the A628 Woodhead Pass and onto the A616. If you still wanted to avoid the M1 (which would be the logical route), you'd need to go via Rotherham. Either way, you'd pick up the A57, taking you through to the A1. That takes you down to the A14 and into Cambridge.
I've driven the Cambridge to Sheffield part of that route plenty of times (although not recently). It certainly goes very close to an RAF base (Alconbury) and passes at least one Royal Mail depot. (Peterborough? Huntingdon?). I'm reasonably confident that you'll see some wind turbines along the route. The A57 stretch has plenty of trees and there are definitely plenty of roundabouts for a while.
That's my best guess, anyway!