It's fixed!
I tried downloading Avast via Internet Explorer instead of Firefox, and a pop up window appeared saying that my security settings wouldn't allow it.
A friend very kindly and patiently on the phone talked me through enabling via the Tools settings what had previously been disabled. I don't know why my settings had changed; his theory was that Avast had told the PC to maximise my security in the absence of any antivirus software, but it is just a theory.
All I know is that I followed his instructions and it's come back.
Thanks again for your help, Ryan. I probably didn't help you by being so vague, but I never would have found these security settings if it wasn't for my friend's prompting in real time on his computer.
Phew, what a relief!
Derek