Such signs have no legal force and are merely advisory. You can, of course, ignore such advice.
Here's one though that would be interesting to do so...
http://goo.gl/maps/Qt6FL
Since the google car visited in May '12, the roadworks have widened, leaving a lane *just* wide enough for an HGV, in one long stretch on the left, with heavy plant and containers/portakabins so no ducking in to the coned area
Going uphill, it is not the steepest but the "average" cyclist would have trouble making it through in the traffic light cycle.
The advisory sign says "cyclists dismount and use footpath" however I doubt that if I were on the trike, that I could actually get it through the narrow footpath, especially where other signs, fances etc encroach upon it - and I'd certainly struggle to dismount and push the trike. No idea how I would cope with this if I encountered it on the trike as there is no alternative suitable road - to avoid it would mean an approx 1:3 hill either up and over the top, or back up after going through the valley below.
Luckily this is only on my "scenic detour" on the way home but it would seem that the only way through would be to stay on the road and meet traffic head on when the lights change