Pudding,
You can get a cargo quote via Trips, in the menu click Cargo concessions. It's not super duper exact, but pretty close. Otherwise the guy at the desk in HQ B side can help you work it out (not sure if that includes pets, but he can definitely tell you and was pretty helpful for me when I was sending personal boxes outside of my repat allowances. Be aware that animals can only go to certain airports in the Uk though