Norwich to Gt Yarmouth. Very circuitous to do without using the A47 Acle Straight. Essentially a death sentence on a bike.
Guisborough to Middlesbrough. Impossible to do without using the Middlesbrough Road A171 Dual Carriageway, unless you use the dead-end NCN 168, and then carry your bike across several stiles and a railway line; British cycling infrastructure, at its finest.
Crossing the Pennines on a Latitude connecting (roughly) Darlington and Shap. Yes, you can do it on some pretty gnarly lanes/tracks, but the default option is the A66, which has zero facility for anything other than motor traffic. To quote a friend from another place, "Stainmore has been crossed by humans for millennia, and now you can only do it in a fucking car". It's a Roman road - there should totally be a non-motorised option. In fact, if I were PM (quite unlikely, TBF), I'd make sure all known Roman Roads had non-motorised access.