Firstly, thank you to all responders. I passed the issue on to Apple Support, and I now have all those apps back in place, and no further updating required.
Should anyone else encounter the same problems I did, here's the solution;
1. Delete each relevant application from the Applications folder one at a time, and empty the trash each time - that is very important I was told.
2. Once deleted, return to AppStore, and enter the name of that deleted application in the search bar.
3. Download the application (click the cloud and down arrow symbol).
4. When completed, open that application from within AppStore, then Quit it.
5. Proceed to the next (old) application and repeat the process as outlined above.
6. When all is done, Quit App Store.
7. Reopen AppStore - all updates should have disappeared.
8. Check your Applications folder to ensure the reloaded apps are in place.
Happy Apping!