Wood pigeons really like eating broccoli, Brussels sprouts and kale. The plants are big enough for the birds to perch on top and eat their way down. It took me a while to work this out; I thought it was slugs until I saw the pigeons at it!
The easiest way to avoid the problem is to cover the plants with netting propped up with sticks or canes. I use woven netting; it costs a bit more but lasts years and I protect it with flower pots or plastic bottles.
The netting also comes in handy to protect fruiting black currant bushes in early summer and, if its fine enough, to keep cabbage white butterflies off the brassicas.