Well, that didn't work. But I have found the problem!
I was using the Dropbox app to copy the public link (via a control at the top). I don't know whether for some reason this generated a different link because when I emailed myself the link for the Index.HTML from my Computer it worked fine! The Dropbox app must generate a different type of URL, one that opens up a sort of download option instead of actually using it. BUt now the problem is resolved as long as email the link to myself!
Not the most practical way but i'm glad it's fixed now!
Could anyone else try copying the link for their app via the Dropbox app and see if that changes theirs too?