Hmm, well small and fast growing in the same sentence makes a good example of an oxymoron.
Any tree planted in a pot, fast growing or otherwise, won't be happy in a pot for any length of time, unless its a patio fruit tree or something similar. That, of course, won't screen you from anything at all.

I'd use bamboo - get tubs 18 inches deep (2 feet if possible) by 18 inches wide (12 inches as a minimum) and plant something like Phyllostachys nigra or aureum in them. These should make between 9 and 10 feet in pots, although in the ground they get to 13 feet.The only proviso is that this isn't really the time of year to plant bamboo, best planted in spring. On the other hand, I see your name is Dartington - if you live near or in Dartington, you may get away with planting now because your area is the mildest part of the country, so unless the winter is very hard, you're unlikely to lose the plants.