When the Euro officials wrote the laws
They never anticipated the wholesale cross border trade we see today.
They only thought cars would be a problem.
So with cars you pay VAT (and other taxes) where you live.
For booze, fags and other stuff you pay VAT where you shop
Amazon are based in a lower tax country than the UK, so people get to go shopping more cheaply there.
This has happened for years. A colleague from Belgium once told me that where he came from on the boarder one side of a road was in Luxenbourg and the other in Belgium. Everything was cheaper to buy on one side of the street, so guess where people go shopping.
The situation with booze and fag tax in the UK has meant that for years people pile down to Dover and hop the channel to go shopping.
Its always been the case that you could phone a shop in another country and buy things straight from them.
It is just that the Internet and online shopping has made this easier.