Opera 51 is now working.
I resolved the issue by downloading and installing all updates via the Linux Mint update tool. Obviously there must have been a missing or dated dependency that was resolved with the update.
The installation of Linux Mint 18 was done several months ago, and the machine was put to one side while I used another old box running Antix. A couple of days ago I decided to move to the Mint machine, and just assumed that Opera would install and run, just as it had done in AntiX.
I've just learned the importance of running updates in a timely fashion....