My sister in the Lakes used to have the same problem. She was so chuffed when she first moved there to have deer, badgers, herons and foxes come in to the garden.
The deer ate all her favourite plants, the badgers dig holes in the lawn, the heron eats the fish and frogs from her pond and the fox leaves stuff for the dog to roll in!
The deer were easiest to deal with....fencing, and high. Anyone leaving the gates open gets a severe frown!