I have now resolved this as follows:

Identified that Pepperflashplugin-Nonfree was Version 21 in Ubuntu repos, as the version of Chromium is 51 and Opera 39 is based on Chromium 52.

To resolve the issue, I downloaded the .Deb file from the PPA available here:-

Note - at the time of writing the PPA owner has not yet added 16.04 to his PPA, so do not add the PPA but downloading the .Deb file resolves the issue.