Almost any fabric with a very tight weave made up of tightly spun yarn will keep a lot of water off and adding a bit of wax or other waterproofing and you can cope with a lot. I've had both cotton and wool jackets/ tops that kept me dry in most weathers. If they haven't been washed in a while, that seems to help and on wool the slight bloom can actually help keeping light rain completely away from the fabric itself. The cut and construction are also quite important. Something like a shoulder caplet makes a huge difference, but even just the lack of a shoulder seam can help a lot. A cotton jacket with a wooly jumper underneath will keep you surprisingly dry, warm and ventilated in nasty weather.
