I have fixed the problem (I think!), I'm just reporting back in for the sake of anyone with a similar problem finding this thread in the future.
It was indeed as we earlier guessed, that a website in my bookmarks had become compromised. And so even though I had not visited the website in a long time, definitely not since it had been hacked, it still was flagged up in Avast when firefox closes - this is I guess because when firefox closes it creates a backup of all your bookmarks automatically, and within that file is the name of the bad website, which must be blacklisted in some way, and so causes the alert.
I fixed it by going through each site in my bookmarks one by one, waiting for Avast to send up the same flag - when it did I simply deleted the bookmark and the problem was solved. I assume visiting the sites in this manner is safe, since avast will stop the threat before it can do any damage, but I am not 100% sure - at the end of the day you are still playing Russian Roulette trying to find a site with a virus hidden in it, so it might be a little dodgy. But it worked for me - Avast flagged it like it should and there were no problems.
I do have a question for Essexboy or anyone else in the know -
Is it possible, had I not had any virus protection, that this Trojan could have done me harm just through 'bookmark backups'? Remember, I didn't visit the infected site; it was simply that my bookmarks were being backed up upon firefox closing, and a bad site was in among the bunch. It seems unlikely to me that anything could have happened, since the site is not being visited, but I just wondered if it is theoretically possible?
Thanks for your help everyone.