Milk alergy in dogs

[OLD MAN OF THE ROAD]

I've read a lot about milk intolerance, but I've never found it in any dogs I've owned. Sandy ,my childhood Cairn had a passion for tea, preferably from a cup. None of my other dogs bothered with it, till five year ago we rescued a JRT/Cairn, who showed an interested in cups of tea/coffee. As she was possibly hyperactive, we thought that perhaps milk might be better. Now its a morning plate of milk. Then all sorts of non dog food, especially noodles and mixer with wet food Fish / wet/kippered and tinned is on her menu, but she eats dog style, some days leaving all. But she always wants a dollop of icecream for her evening treat.
Spoilt, yes, but she never gets more than 8kG, and is like a mini greyhound in park.