Are you accessing it using Samba or FTP? It sounds like you're using FTP in which case you would have to download everything to use it, but with Samba you should be able to run files from the shared drive.

Edited: I've finally cracked it. But problems below were very real. I'm setting up a post with my list of things to do to make it work.

I'm using FTP because I couldn't make Samba work. I'm on Windows XP home; should I have some Samba product on my PC? Here are my problems...

Going through the set-up PDF document, I don't have the NetBIOS name service section of the USB General Settings.

In part 2 this bit baffles me (I assume 2710 instead of 2820):
"1. Choose any one of the computers in LAN of the Vigor 2820."
What is a computer in a LAN? I've just got one computer (at present), the router and the USB drive.

"2. Open any browser and type "\\192.168.1.1" (without quotation marks) in the address bar, and then click OK. The files available on the USB device will be displayed as "Vigor 2820 Samba Server"."
Typing \\192.168.1.1 just gives page not found errors. I've tried it in IE, Firefox and Windows Explorer both for a local drive and the ftp USB drive which I can now access. In fact I've typed it into every address bar I can find - same result, and I've tried \\ and //

I'm determined to make this work, but there really should be a decent set of instructions somewhere that assume the user knows absolutely nothing about networking and the stream of acronyms and abbreviations.

Just type 192.168.1.1 in the URL bar for IE or Firefox and that should give you the Vigor router. I agree ALL the Draytek documentation is poor and assumes you know everything already. If you did you wouldn't need the documentation!

It turned out to be Zone Alarm. I've now written up my experience here:
http://www.forum.draytek.co.uk/viewtopic.php?t=13788