The A46 (now defacto motorway between Leicester and Newark) between Widmerpool and Bingham appears to have a gated service road - I keep meaning to try it, and then between Bingham and Newark the old A46 is a good quieter route.
I believe that parts of the previous A1 around Peterborough are now cycle-friendly.
These roads are certainly worth knowing about, and it would be a good idea to have them documented. The devil is often being able to access the 'good' road without having to use the 'bad'
Next to the new A46, north of Widmerpool, there is a bridlepath between Kinoulton and Owthorpe, but part of it is unsurfaced, so it’s a bit of a slog. From Owthorpe going north, the old main road is still there, apart from the bit between Cotgrave and Stragglethorpe is missing (buried under the new road). You can divert either via Cotgrave or Cropwell Bishop to Stragglethorpe. From Stragglethorpe to Bingham, the old road is still there and a lovely quiet cycle. The road from Bingham to near Car Colston is still there but is used by local traffic. North of Car Colston, the old road has been turned into a cyclepath as far as Red Lodge, then it disappears under the new road, but they have built a bridlepath on the north side of the new road, to Flintham, where the old road reappears and can be cycled all the way to Farndon and Newark.
I do many of my local rides on the Old Fosse Way, as I only live about 300 yards from it at Bingham. It’s much more cycle friendly than it used to be and the junctions on the adjacent new road are graded, which means you just cycle over or under It. We used to have to wait minutes for a gap in the traffic, when crossing the old A46 between East Bridgford and Car Colston.
Years ago, we used to cycle on the Old Fosse Way from Sharnford, south of Leicester all the way to Halford, on the edge of the Cotswolds, when going on hostel weekends.