The first thing you will need to figure out is an alternative to milk, especially if you are a fan of breakfast cereal. Soya milk is a good option to start with, but more and more dairy-free milks are appearing on the supermarket shelves. See Milk Alternatives for some other types of plant-based milk. My absolute favourite for tea and coffee is Oatly Barista. It has a bit more fat than the standard oat milk which makes it 'foamable'. This also happens to make it mix really well with tea and instant coffee. Of course you can also try other teas that don't need milk such as peppermint, chamomile, and green tea.
To replace butter on your toast and in sandwiches there are a few dairy-free options. My favourites are Pure margarine, and Flora plant-based spread. Incidentally, Flora have recently announced that all of their products are going to be plant-based. At the time of writing the Flora Buttery spread does contain buttermilk (even though it used to be dairy-free - boo!).
Thanks to the popularity of plant-based foods, in recent years there has been a huge improvement in vegan cheese. Ten years ago they were mostly made from soya, and they were pretty awful. Now they are normally coconut based and can be found in supermarkets in block form, sliced, or grated. Cathedral City even have a plant-based cheddar now which has had mixed reviews, but I really like it. There are some great vegan mozzarella-type cheeses that melt really well, and slices of what I call 'plastic burger cheese' that are just as good in a burger as the dairy ones. The downside of these is that they are not quite as good nutritionally as 'real' cheese, as they are lacking in protein. Another type of plant-based cheese is made from nuts, such as Mouse's Favourite. These are a bit more specialist (and expensive!) and you won't find them in the supermarket but they are worth seeking out. I am lucky to have a local vegan deli which sells them.
I spend a lot of time looking at labels in the supermarket. It's a bit daunting at first but you will soon get to know which foods are safe. The good news is that since milk and eggs are common allergens you will see them in bold in the ingredients list. You can also look out for foods labelled as Vegan or Plant-Based, although it is still worth checking the labels depending on how sensitive you are to dairy. Sometimes you will see May contain traces of milk or This product is not suitable for people with milk allergies to due manufacturing methods.
Milk can often be found in places you wouldn't expect. Here are some to watch out for:
Egg can also show up as a sneaky ingredient.
Pills sometimes contain lactose, so make sure to read the label. Look for capsules, for example paracetamol capsules with the plastic-type coating may not contain lactose whereas the traditional 'chalky' pills do. For some medicines, such as antihistamines there are liquid alternatives. The quantities of lactose in medicine is normally very small, so it depends how sensitive you are to lactose. Ask your pharmacist for advice.
If you cook from scratch you are on to a winner. After all, most food is dairy-free to start with. See the Recipes section for some ideas.