Hello, I'm an experienced health visitor and I just wanted to give you some advice.
There are a few methods that i would recommend that work that you can use depending on your parenting style and also how old your child is I know you have said 2 but 2 years 0 months is very different to 2 years 11 months! But people still peg them on the same age bracket by just saying 2 years old!
If your child is capable of understanding, (they probably know more than you think!) Spend the next couple of days talking and explaining that mummy is not going to give you milk at night time anymore and that milk will come at breakfast, be nice about it but firm that that is what the goal is. If your child is interested back this up with stickers or other small rewards for not crying for milk in the night.
Method one: offer less milk over a few nights, so assuming that they have their milk in a cup of some kind, just put a wee bit less in over a few night until it is not worth waking for. I have known this method to work but from experience it is not the most effective!
Method 2 : water it down. Assuming that your child is getting enough vitamins and nutrients through food during the day now, it is absolutely fine to water down full fat cows milk, again over a few nights make the milk more and more watery until it is just plain old water! The good thing about this one is once it's water you can put a cup of water in or near their cot or bed so that any waking in the night they can independently get themselves a drink. The only issue with this is it will need to stop when toilet training starts in the night.
Method 3: cold turkey- lots of parents don't like this one but from experience it is the quickest way. Just don't respond with milk at night, be prepared, there will be tears but these don't usually last more than a few nights with the first night being the worst. Remember to prepare your child by explaining what is going to happen, do not surprise a child of this age as it will only lead to confusion and anxiety as to why you haven't appeared with milk for them.
HTH OP - 2 year olds are hard but most of it is creating solid boundaries and standing firm, hope you get some sleep soon!