Put the milk, garlic and anchovies in a small saucepan over a low heat and cook gently for 15 minutes, without letting the milk come to the boil, until the anchovies have melted into the pan and the garlic is soft.
Use the back of a fork to mash the garlic against the side of the pan. Add the butter and oil and stir until the butter has melted. Transfer to a small serving bowl.
Arrange the crudités in a large serving dish, leaving space for the bowl of sauce, and serve while the sauce is still warm for dipping.