OK, I think I wrote about the solution to my problem too soon.
The new version of Adobe Reader for Mavericks appears to assist with the viewing of existing PDF documents that you have already downloaded, and offers improved options to manipulate, or edit these documents, although the issue of downloading a new PDF document from a web site remains.
In addition to my earlier comment, my experience upon downloading a PDF with the new Adobe Reader in Safari 7 is that the web address appears in Safari, with the browser appearing to load your file as the blue beam moves from the left to the right. On other occasions the web sites visited indicate that Adobe Reader is blocked from this site, with a grey message box appearing in the centre of the screen, which is accompanied by an arrow that points to the right.
If you click on the message box, an additional loading message box is generated towards the bottom of the browser, indicating the size of the PDF, and it's downloading status. This reflects the blue beam that appears in the web address field that indicates when new pages download, or the PDF in question, but the files continue to take a very long period of time to download, if at all.
I am keen to keep using Safari 7 in Mavericks, but this is very annoying, particularly if you are a time poor higher degree student who is trying to complete a research dissertation. Almost every academic document, or scientific paper viewed is available in a PDF format, and no doubt most users can see that this issue creates additional problems if you need two, or three web browsers to download the specific paper you are wishing to read.
Is there a easier solution ? I appreciate that Safari 7 offers improved security from Internet nasties, but this new browser is preventing me from completing my work. Would it be possible to return to an earlier version of Safari, without wiping one's hard drive ?