A council tip near us most often has a queue of cars so long that I'm sure it would take anyone half an hour or more to get as far as the skips. This isn't likely to help the fly-tipping problem. Faced with a queue like that, it must be very tempting to find a remote spot and just off-load items that are too large for normal refuse collection. I think there ought to be a free 'once a month' large item collection. Designate a spot at the end of the road where these items can be collected from. Then people might not be so inclined dump their old furniture in a lay-by or elsewhere in the countryside.
I'd never condone fly-tipping or do it myself but the poor facilities certainly don't encourage people to get rid of their unwanted items legally and in the right place. We ride our bikes in some 'out of the way' places and so see quite a bit of fly-tipping. A couple of examples: