I get it sometimes, and while milk is a base, you'd have to drink a helluva lot to get it to counter the acid. One glass alone does not do the trick for me, and by then, I'm pretty sick of milk.
You can alleviate it by taking rolaids or tums (if they have a different name in the UK, someone should correct me), which are little tablets/chews that counter the acid.
You can prevent it by avoiding foods that commonly cause it - oily, fatty, fried foods are common causes, as are tomato products and, for me, complex carbohydrates like bread.
If it is really bad all the time, go to the doctor and he can recommend something more hardcore and/or give you a prescription.