Stone is now a 'folk' measure. People still think in them and use them, but all 'official' uses (health records, for example) are kilograms.

There are still a handful of official uses of imperial. Miles for driving, as you say, pints for draught beer etc. in pubs, miles and chains for railway distances, maybe a few others. More cases where the labels but not the size have changed, like 568g jars of jam.