Dairy-free means no lactose. So as long as you do your research you should be looking to avoid any ingredients or food items that contain lactose.
But be aware, lactose doesn’t just come in the expected items such as milk, cheese, yogurt and chocolate. You can also expect to find lactose in cakes, biscuits, boiled sweets, some ready made cereals and even some processed means such as sliced ham.
Be sure to do your research and find a list of alternatives and items to add to your avoid list.