Does anyone know of any (preferably free) software which I can install to allow me to view all of the websites that computers on my home network have accessed?

Anything of this sort would be great. Thanks.

Your router would be the key to that, since all traffic will go out through it.

After a bit of searching <monitor + router + traffic> on google, this looks most promising.
Paessler's PRTG monintor program:
Information
Freeware Version

Great, thanks.

I have never heard of it before!!
Thank you very much!