I take it your dovecote is empty & there for decorative purposes.
I quite often see a pile of feathers in my garden & know the local sparrowhawk has visited. They only kill when hungry, so if I do see one with its prey, I try not to disturb it or it will only kill again.
I keep & fly a small breed of pigeon & if they stay in the air, the sparrowhawks are not a threat, but sometimes the sparrowhawks can drive them down to the ground so that they can catch one. The female sparrowhawks are the main threat to them because they are a lot larger & more powerful than the males.
I sometimes also have a problem with peregrine falcons, - when my birds are flying high, they can be seen for miles & attract the attention of the peregrines, once they are in the area, I can almost guarantee that at least one will be taken.
I dont particularly like birds of prey because its not nice seeing my own birds get taken, but they have to survive so its a case of live & let live.