Same Neighbour, (Mick Willis - former Bargee in B'ham), same time, we had a 6 month old Ginger Tom Kitten ... every morning about 8am, he'd return across the fields with something. Mick would watch from the bedroom window to see what it was. Crow, Pigeon, Squirrel, Mole, Dog Bone, Sunday's Chicken carcass, Mouse, old Bicycle tyre, anything he thought that would make me a good present. He'd drag it into the hall and sit at the foot of the stairs making a particular 'look what I've got' meow. How he got some things through the cat flap astounded my family.
Prudence, our other cat, (famous, was in the B'ham Mail !), used to bring in live rabbits. Never harmed, just picked them up, bought them in and let them run around in the house. This lead to me and a pillow case hovering over a lettuce leaf at 1am waiting to catch a rabbit who was hiding under the fire/settee/dresser, etc., on many occasions.