the law generally allows this, but the law needs updating as it was set when fewer and slower cars were on the roads - cycling on duals is essentially suicidal
I remember as a teenager during the long, boring summer holidays going out on a bike ride and ending up riding along the A1 south of Bawtry (I lived near Gainsborough) - perfectly legal, but even then a bit scary as the traffic had just come off the A1M. And of course nobody had heard of hi-vis and helmets back then. This would have been the late-70s / early-80s.
I wouldn't do it now, and if I'd had the risk awareness I have now I wouldn't have done it then.
Hand in hand with fast dual carriageways you also get fast roundabouts; even if you're on a bisecting route, you can still find yourself mixing with DC traffic. Sorry, but whatever my rights might be, there are several fast roundabouts I avoid. Even cycle paths routing cyclists over the entry and exit slips aren't safe - e.g. the recent fatality in Manchester at a light-controlled crossing.
My guide to the roads I avoid goes along the lines of; think back to when I was 20, and what my driving was like. Would I have wanted to be cycling on the same road as me? I've learned a great deal about risks since then, but there's a new generation of inexperienced drivers, plus the perennially stupid!