We have a Burford Holly that has grown "out of control" for a long time. It is more than 12 feet tall and has lots of these red berries. We have never seen anything eat the berries, so they remain on the bush for a long time!
Perfect flashes of red on your Burford Holly. Ours are out of control too, but they make a nice privacy screen along the back fence, so we let them tower. The birds will start to devour our berries after they soften towards spring.