I have built raised beds on my lottie which had been very overgrown and also has rather poor chalky soil. They are about 6-8 inches deep and I did lay some weed suppressing membrane as a base. I filled them with mushroom compost, manure, old growbag compost. I grew cabbages, spinach, beetroot, leek, broad beans, onions, shallots, brussel sprouts, cauliflower etc. succesfully. I still got weeds forcing their way through but not too many. My hope is to eventually pull away the weed supprssing membrane after most of the weeds have given up (well, I'm hoping). For potatoes, carrots, parsnips I guess you'd need deeper beds.