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Not all A roads are like that (some of them are like this: http://www.sabre-roads.org.uk/wiki/images/9/92/A26_junction_with_Blackboards,_or_Orrisdale_Road_-_Geograph_-_1845748.jpg ) but you never know when the reasonably sleepy two-lane A road you're riding on is going to lead you onto a monster dual carriageway
I use a level 0 google street view recce of a proposed route for this. You don't actually go into streetview, you just start draging the man so that the blue lines showing where streetview is available appears. Dual carriageways show up as double lines, and as a bonus "cycle routes" that are actually more like dry stream beds tend to show up as having no street view.
Some A roads are ok, some are really awful. A lot of them are functionally identical to motorways without a hard shoulder. Aseasyasridingabike has a visual comparison to this effect: http://aseasyasridingabike.wordpress.com/2014/03/06/more-motorway-idiocy/
Not all A roads are like that (some of them are like this: http://www.sabre-roads.org.uk/wiki/images/9/92/A26_junction_with_Blackboards,_or_Orrisdale_Road_-_Geograph_-_1845748.jpg ) but you never know when the reasonably sleepy two-lane A road you're riding on is going to lead you onto a monster dual carriageway with HGVs thundering past with centimetres to spare, so they are indeed to be avoided like the plague unless you're already familiar with the specific roads you're using and know them to be the ok kind.
FWIW routes using B roads tend to be nicer and a bit shorter, in my experience - you don't end up doing sweeping diversions around little villages and can go from A to B (hah!) more easily. Means more time for beer and nicer scenery on the way there.