I think they really need to target the employers. If they make the risk of getting caught far outweigh the benefits of employing these people then employers would think twice.
Where a business is caught with say more than 2 or 3 illegals then it is obvious that it is their policy to employ them. So then you should say if you are caught with 3 or more the fine is increased to £50,000 per illegal this would make them think again. Once you start aggressively targeting the employers then the message will start to hit home.