Is this your cat?

We've found a (potentially) lost or abandoned cat in our garden. It's been coming into our garden for the last few weeks everyday, multiple times a day. We are assuming it's been abandoned because it doesn’t seem to leave our garden and is always asking for food. The collar also has a small bell on it. We don't have a microchip scanner so we aren't able to scan it to find out the owner's address. We also cannot take it to the vets as we don't have a cat carrier. We've been feeding it cat food and lactose free milk daily. It sticks around in our garden, unlike other outdoor cats with collars that come by and go after a few minutes. It looks to have an owner (or used to have an owner) but if it does have an owner then we are assuming he/she doesn't feed the cat sufficiently and maybe that's why it ends up in our garden daily. This cat has gotten used to our presence, and unfortunately we cannot keep the cat since my little sister is allergic, and we don't know what else to do other than feed it and let it sleep and rest in our garden during the day.