I clean my Cotswold fleece by first shaking the fleece nice and hard for several minutes to remove as much vegetable matter (VM) as possible. It's amazing how much VM comes out just from shaking. Those beautiful curls unfortunately can hold (and hide) all sorts of bits of hay and stuff.
I wash it pretty much as wool from any other breed of sheep -- using hot water and mild soap. I start by soaking the fleece in plain cold water two or three times. A lot of excess dirt and sweat come out that way. Then I put the wool in the soap and hot water, letting it soak for about 10 minutes. (Don't let the wash water get cold; the dirt and grease will reattach to the wool.) Next, I remove the fleece from the wash water and put it in clean water to rinse it. I usually perform the rinse process at least twice, sometimes three times, until the rinse water is clear.
In general, I think you have to worry less about felting with Cotswold wool than with some finer wools. It can felt but not nearly as easily as Merino, for example.
Lay the wool in a sunny, clean place to dry. Placing it on a screen or a chain-link gate on the ground allows air to circulate and dries the fleece faster.
After it dries, you may have to remove more VM (those curls, again). Opening up the locks a bit and shaking again can help with that.
Remember: when washing any wool, do not agitate or wring the fiber. Don't temperature-shock it (i.e., don't put it in hot water and then immediately in cold water or vice versa). Don't let water run directly on the wool; fill the wash basin with water (and soap) before you put the fiber in.