The guidelines recommend using [P]with the brackets. After some testing, UK editors felt that this actually looks quite good on the client. Waze doesn’t do anything special with it though.
Also note that only public car parks should be labelled like this, not customer car parks for shops, etc.
I like to think customer car parks are no different to council owned ones so they should be added. Large out of town retail parks, shopping centres etc, all aids with navigation.
Plus all free private customer car parks have unlimited parking, no need to worry now they can’t tow or clamp. Useful if you need to find a car park.