I came across this term at an English train station. My friend and I were looking for a place to store our luggage and it didn't occur to us that 'left luggage' was the place we needed to go as it seems like a place for lost property. Why does it have this confusing (for a non-native English speaker) name? What's the origin?
Well there's a logic to it: if you want to leave your luggage somewhere for a while, then the luggage will be left, i.e. it will be "left luggage".
Yes, it is ambiguous. It's not just non-native speakers who have the problem; as a native speaker I assumed "Left luggage" meant "Lost property" until I was about 20 years old.
"Left luggage" is a place where you can leave your luggage. Where major stations (in the UK) have a left luggage facility it's usually run by Excess Baggage Company and they contract with Network Rail to also offer a lost property service. The Excess Baggage stores have storage and security screening facilities.
Other stations may have a "lost property" facility but it won't be open to the public and in some cases property will be taken elsewhere to be stored.
On the other hand, Transport for London have a "lost property" office, but they won't let you leave your luggage. It is therefore not a "left luggage" office.