One has to be careful for that which one wishes. Nature is not always nicely selective ;) We have field mice, mice, rats, slow worms, grass snakes, vipers, toads, hedgehogs, a badger that woke us up one night and others unseen that just got the lawn up. Foxes and deer.
Birds as one might expect but also owls perched in the trees at night, sparrow hawks quite often, a buzzard has come down onto the back garden and we had an awkward heron than perched on the ridge tiles, much to the annoyance of the dog for quite a while. We had a poor old racing pigeon resting on the roof for over 24 hours and eventually I managed to catch it in a cage and that enabled us to read its ID ring on its leg. I rang the owner in Barnstable, Devon who wanted me to send it back to her via courier. "Barney" stayed with us for a couple of days and was well rested and fed before I released him - he spent an hour or so on the roof before flying off looking quite strong.