I only grow what you call mangetout (we call them snow peas or snap peas, depending...).
I am assuming KW peas (field peas? Someone set me straight if that's wrong) will vegetatively be just like snow peas. They will climb up once the tendrils touch something they can latch on to. I usually put in my strong support up, sow peas (or plant seedlings) next to it, and place a very loose thicket of twiggy branches over them. The peas latch on and up they go.