Thanks for the suggestion Ebenchich.
I don't think this applies to me though because I am running the site from the subdirectory as well (not the root). The rest of my site is powered by Coldfusion - it is just the one directory (in the original post called /wordpress/) which is running wordpress.
I am guessing there is something in the W3 Total Cache plugin php which I need to modify to allow for this. Unfortunately I don't know how!