I've seen many VM users reporting similar problems in the Tech Support newsgroup, particularly
with the BBC iPlayer, and it seems that using a proxy frequently
provides a workaround.
You sound like you 'know your way around' but for the benefit of others:
To set up a proxy in Firefox, go to Menu/Tools/Options and select the Advanced icon at the top and then the Network tab.
Now select Connection Settings and click on "Manual proxy configuration", enter webcache.virginmedia.com as the HTTP Proxy and 8080 as the Port, and click OK and exit.
You may need to restart Firefox (or even reboot) for the changes to take effect.
I'm sure other browsers will have similar options in the configuration section.
Many routers also have the facility, which could be useful for problems with other http applications and multiple devices.
Good luck!