Which one is more British: "car hire" or "rent a car"?

I am wondering which one is more commonly used in the United Kingdom: car hire or rent a car?

In British usage (at least up to the last few decades)

• "rent" is used for (real) property only: houses, flats, offices, factories
• "hire" is used for any kind of moveable property: cars, costumes, marquees, glasses (for a party), scaffolding, chainsaws ...

("hire" is not used for people: rather "employ" or "engage").

I qualified this because American usage is now recognised here, and I would guess is used by some people.

But "car hire" and "hire car" are both common expressions still.

I would suggest that car hire is more common in the UK.