For once I agree with Marinyork. Cyclists are allowed on A roads and it's personal choice whether you use them or not. If I'm on my own, I tend to take the direct route from a - b which often involves A roads. I think the busiest I've been on is the A2 at Gravesend in Kent which is just after it has been declassified from the M2 (there is no change in the road or the traffic, just a sign saying end of motorway). I was once asked, very politely, to leave by a Highways Agency man who admitted he had no right to ask but said he would feel more comfortable if I did!
I cycled up to town on the A2 about 15 years ago and vowed never again. The A2 from Rochester as far as Bexley is a motorway in all but name. (with 4 lanes in parts) Not too bad I suppose if you cycle on the hard shoulder, but I found the issue came when you had to go straight on when there was a turning off. So although a legal right, I am not sure it is one I intend to exercise. As for taking primary!
Fortunately there is a lovely alternative now, as the old A2 between Shorne and near Ebbsfleet has been turned into a dedicated pedestrian/cycle route. This is very wide for most of the way, thereby minimising issues with pedestrians and dogs.