Oh trixy I didn't know that about those tesco crisps! I'm always looking for child friendly crisps as I cater whenever there is a party at dd's toddler group so that the food is allergen free. I wonder if they have a "cannot guarantee ingredients are but free" as so many tesco products seem to have that. I'm going to check them out.
For children's parties, asda's own brand pickled onion monster bites are milk free - you need to buy the big sharing bag as opposed to the multi pack as our flavours contain milk. Dd loves them as she thinks they are monster munch.
If you are looking for other party food aswell as crisps, Asda's value range frozen sausage rolls are milk free. They are extremely cheap but are tasty to have at parties and no one will know you have gone for the cheap option.