There will be those much more expert in this than am I, and who know what the regulations currently say. As an outside observer, I think there's a greater tendency to consider other traffic now and, to go back to my original example, therefore a reasonable chance that, had the A11 been designed now, it would not have been done in a way that cuts the main route between Cambridge and Norwich for some traffic.
That said, provision can be highly variable and, for cycling-specific routes, budgets create a great temptation to compromise and build very poor quality, indirect routes on narrow, bumpy tracks with lots of stop-and-give-way crossings which, for any distance (again, riding from Cambridge into Norwich is a good example), would be virtually impracticable to use.
Of course, people actually riding those distances must be a tiny fraction of a tiny fraction of 1% of all traffic, so really hard to include with tight budgets, so it's easy to get unrealistic. I suspect that many of the roads alongside the A1 that I mentioned have actually been left there for a range of reasons, with cycling being no more than one possible factor - even though, for me, they are preferable to dubious cycle-specific provision. No-one is going to build a whole road specially for long-distance cycling - it's just nice if they don't obliterate an existing one, or leave out a 100-metre cut-through section that makes a vital connection. But the M25 experience showed, I think, that a road designed for long-distance travellers could in practice attract local traffic as well. I don't see why that shouldn't apply to local cycle traffic - so maybe we should talk about Mildenhall being cut off from Thetford, which it is. This brings the possible effects on local cycling more to the fore, of turning a highway (which is arguably a road for all travellers) into a dedicated motor-only road.
I'm not sure about your A131 example. Probably, the funding was only there to bypass Great Notley and then Great Leighs. I can't really see the remaining section, and all similar roads, having dual-carriageway bypasses that leave the old road in place. Paths alongside, maybe. But you're right about the way that road improvements have knock-on effects; the dualled sections will undoubtedly have increased traffic, and speeds, on the remaining parts of the road. That's an example of how improving one piece of road creates problems elsewhere. No doubt the residents of those two villages are still glad of their bypasses!
