In many circumstances, "supermarket car park" is preferable. I guess there is a slight fussiness or awkwardness associated with "supermarket's", so we try to avoid it if we can and use the noun "supermarket" attributively instead. Also, "supermarket car park" seems more like a description of the place in its own right, rather than as a place belonging to a particular supermarket.
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Anonymous which is correct:
supermarket car park
or
supermarket's car park
Why?