Can an online store know your age from your bank card?

I am worried about a friends duaghter who is under age buying fags from the internet, as she is a lovely girl and i want to help he give up smoking. I am wondering whether she is using her mum's bank card or something, as it thought the company she is buying off who are strict about minors would be able to tell that it is someone underage?? The stuff is send by royal mail ( we live in the UK ) not a Currier. Can an online store know your age from your bank card??????????