I don't drink milk, but I was a regular at Lemon Farm in BKK when I lived there. Tons of organic and natural products and quite a few locations. It's owned by one of the princesses and all the proceeds go back to the farms that grow their produce and the people who make their goods.
They've changed their website and it's all in Thai now. Welcome to Lemon Farm
Here's a writeup in English that talks about two locations on Sukhumvit. Where to Buy Organic and Pesticide-Free Produce in Bangkok - Associated Content - associatedcontent.com