I believe the Easy Care Breed is a cross between either
Wiltshire and the Lleyn and there is the wiltshire and the Welsh Mountain Sheep.
The wiltshire not requiring shearing and the Lleyn being a prolific lamber
I think the welsh mountain sheep was chosen because of its qualities.
It was a cross between a Nelson Welsh Mountain and a Wilts, I think, Lleyn blood was added later to make them more prolific and presumably breed the horns off (Lleyns are double polled). Has then been bred to type for generaitiions - Iolo Owen won the nobel prize for it.
There are lots of shedding composites around now, since its actually genetically not that difficult an operation to breed the wool off. I breed mine out of a Wilts and a Lleyn (mostly).