My Firefox updated fine as well. If something interfered with the update, it might have caused a problem, and it sounds like something DID interfere. If AVG had blocked the download or prevented access to Firefox by their site, I'd think you would have received a message.

You said,

"All has been well so far but yesterday whilst trying to connect to the net, a message flashed up for a second or two, which said Firefox would update itself. This quickly disappeared and I was left looking at my normal desktop.
When I tried to connect through Firefox again, a few seconds later, "

It's possible you interrupted the update. If I recall correctly, Firefox downloaded the update then shut itself down to install it. Maybe you interrupted the install and tried to open Firefox before it was complete?

I'd go the less invasive route first, because when you uninstall Firefox, you lose your bookmarks, history and all the other user-defined stuff.

I'm cautious, and I'd try the following (including some things people have already recommended) until something solved the problem.

I'd just try re-booting first
Then I'd try to re-install
Then I'd try downloading the latest Firefox and installing over the inoperative version
Then I'd try a clean install (uninstall, then install the new, downloaded one)