Hopefully this does not fall on the wrong side of the new specificity rule. I think this is a pretty specific question, so I'll try to define my terms:
By "ethically" vegan, I mean cultures or people that had ready access to animal-derived food and goods but who consciously declined to utilize them because of ethical considerations regarding the commodity status of animals. Cultures that had no ready access to meat or animal products (if any existed at all), I would not count as being "ethically vegan". And by "vegan" generally, I mean people who make an attempt to eliminate (or at least severely limit) their usage of meat and goods. For the purposes of this discussion, I'd define someone who simply doesn't eat meat (but, for example, eats fish or food made with milk or eggs, or doesn't check to make sure their beer isn't filtered through animal products) as Vegetarian but not Vegan.
The Wikipedia article for veganism mentions several ancient Greek philosophers who were vegetarian based on their beliefs, but the article does not mention whether they were vegan (nor does the preview for the paywalled source it cites). I would assume that they would still possibly eat eggs and use contemporaneous leather products (otherwise, I would expect the article to say so) and possibly things like vellum (if that was invented by then; I'm not sure).
So given these constraints of (what I would consider "modern") veganism, were there any historical cultures that adhered to these ethical restrictions?
Many followers of Buddhism, specifically in China and Tibet, follow a doctrine of non-violence, which extends to not killing animals.
An example of this is the story of the wild goose pagoda in Xian. http://www.travelchinaguide.com/attraction/shaanxi/xian/bigwildgoose.htm Now this doesn't strictly say no milk or honey, etc., but it provides some ethical backing to not harming animals.
The Cathars in southern France and northern Italy during the 11th-13th centuries were vegetarian (not vegan) due to certain theological beliefs. Interestingly, their meat eating, northern brethren invaded and fought them in what is now known as the Albigensian Crusade.