Huge slugs in my garden!!!

  Unlike lots of women in Russia, I am not afraid of mice, snakes, I can even stand seeing a cockroach without fainting.

  In fact in my eventful life there were times when I used to catch mice with nearly bare hands - well, I had my hand wrapped in a plastic bag (or, rather, had a plastic bag over my hand) and was chasing after mice all over my room in the students' dorm. I caught about 20 or 30 of those squeaking monsters. Not every cat can boast of such heroism and that many trophies.
  All cockroaches in the neighbourhood knew I wasn't the one to mess with - I killed them with cold heart and slippers.
  But before moving to the UK I had never seen slugs of this size: they are huuuuuuuuuge! They are fat and disgusting.
  They live in my garden and happen to think they can treat themselves to my cat's food. They scare my cat and disgust me.
  If anyone knows a way to get rid of them for good, please let me know - they attack my cat's bowl which is outside at the moment because it's nice and warm. They come in the dark, quiet, disgusting intruders.
  Please let me know: my cat will be grateful :)