Short answer: No, ASDA’s Milk bottles are not vegan-friendly.
ASDA’s Milk Flavour Bottles 50g are not vegan or vegetarian because the product contains gelatine. This is derived from the hides and bones of pigs, cows and other animals.

Here are the ingredients: Sugar, Glucose Syrup, Maize Starch, Beef Gelatine, Flavouring, Sunflower Oil, Glazing Agent (Carnauba Wax)