Thanks for the swift replies.
The iMac is a private computer which I use primarily for score-writing: it was last used on 14th Sept. No-one else had access to it. I use my MBA for Email and general use. I checked my Downloads folder, and there's no sign of Avast being downloaded. There's no sign of activity at all during the week until the work I did yesterday (24th). In the Apps folder, Avast claims to have been created on 23rd Sept. No-one was at the computer at that time.
I have never felt the need for anti-virus software on the Mac, so I am as certain as I can be that I have not (knowingly) installed Avast in the past. Indeed I didn't even know what Avast was when I found it, and had to look it up.
What other installations might let Avast in?
Thanks!