Thanks for the reply, but I just fixed the problem this morning! I have installed a couple of apps a while back but was unsure if they were the cause. Rather than do wholesale uniinstalls, I read about this technique:
As soon as you notice an unwanted full screen ad popup...
1. Go to Play Store on the phone.
2. Click the 3bar Menu icon at the top of screeen.
3. Select "My Apps & Games"
4. Select "Installed"
5. Select "Last Used" on the sort sub-menu.
Notice which app has been started in the last few seconds or minutes. This will probably be the one that initiated the popup.
I did this and noticed that "QR Scanner" from G-Tool Lab had run a few moments ago, even though I had not run it myself in several days. I de-installed that app and the problem is gone!