Well this was fun... All the examples of how to connect through a proxy from SharePoint are missing a crucial piece of information!
<system.net>
<defaultProxy>
<proxy usesystemdefault = "false" proxyaddress="http://proxyservername" bypassonlocal="true" />
</defaultProxy>
</system.net>
This is the accepted route, with an exception to e added to the proxy to use anonymous authentication...
But is you use:
<defaultProxy useDefaultCredentials="true">
<proxy usesystemdefault="false" proxyaddress=http://proxyservername" bypassonlocal="true" />
<bypasslist>
<add address="[a-z]+\.domain\.biz" />
<add address="[a-z]+\.domain2\.biz" />
</bypasslist>
</defaultProxy>
The required bit of which is the useDefaultCredentials parameter that passes the logged on users credentials on to the proxy server.
Now all I need to do is get the double-hop authentication to work...