No, definitely not part of a default installation of Firefox.

You can disable any extension here:

orange Firefox button (or Tools menu) > Add-ons > Extensions category

If the extension has a Remove button, you can remove it immediately. If it does not, then it was added to Firefox externally and often can be removed through the Windows Control Panel. Of course, the trick is figuring out how it is listed (e.g., under what name or as part of what software).

In some cases, you need to hunt it down and delete it manually, but let's come back to that if needed.

Perfect guidance. Thankyou.

There was no "Remove" button, and a search using online guides for files and dlls produced no results. However on your suggestion I searched the installed programs and found "Search Enhancement Tools" which I had NOT installed and which was not in my programs menu. I removed this, and on relaunching Firefox found miraculously that a "Remove" button was now available. A click and a reboot and its gone from the extension list.

Now the big questions. How did this little bugger get past AV, anti-spyware, anti-malware and firewall, how can we be sure that all traces of it are gone, and how do we prevent it installing itself in the future? More to the point, how can this company get away with doing this?

A lot of "free" software has unwanted software bundled it. Often there's a checkbox to avoid it, but often not. Unless you keep careful track of everything you install, it might be difficult to track down the culprit.

Very aware of this.However I have installed nothing for months, and am particularly cautious with all installations anyway, and I never ever install toolbars. This is a recent encroachment and has found its way onto my system surreptitiously. It seems to me that it would be ideal for many Firefox users who may be similarly afflicted to understand how it might have gotten onto the system and how to prevent that from happening in the first place.