Trawling through Google support pages there are confusing references to transfering ownership (only if you're currently listed as a manager or can contact the owner) and verifying businesses but nothing written in plain English about how to claim ownership of an existing listing without contacting the owner.
Here is it in plain English:
1. In your Google Business account create an identical listing to the one that exists under a different owner
2. Google will identify this as a duplicate listing
3. Google will present you with a form to submit a request to the current owner to take Admin rights of the existing listing.