I agree with tiercel, in a straight flight a pigeon is faster than any of our uk birds of prey. Peregrines catch them by falling not straight flight. Sparrowhawks mostly catch them by ambush, flying stretches of gardens and dropping on them as they appear over a fence. Sparrowhawks are much faster than buzzards and red kites, I've had first hand experience flying Sparrowhawks and next to blackbirds pigeons are the hardest quarry