Are you allowed to park...

[SoupDragon]

... a caravan on the road? I always assumed not because it's not taxed.

My holier than thou neighbour does, and also facing the oncoming traffic.

the facing the traffics not allowed though...hmm dunno

This is facing the direction of travel

But it still irritates me because if you parked an untaxed car which is smaller than a caravan it would get towed away and probably crushed.

yep according to this after a quick google

Well done. Good googling skills
I wonder why you're allowed to do that if you can't park an untaxed car there... strange.