Apache mod_auth and mod_proxy not working together

I am trying to set up apache as an authentication front end for a web backend running on port 8080. The backend has no authentication, so if you curl localhost:8080 you get the website. Port 8080 is blocked externally, so what I want is for apache to authenticate a user accessing from port 80 and then proxy to port 8080.

I believe this should be possible, as per this post on stackoverflow:
https://stackoverflow.com/questions/724599/setting-up-an-apache-proxy-with-authentication

I have tried to replicate this, however, I cannot get Apache to authenticate; it just passes directly to the proxy. Here is the virtual host config:

<VirtualHost *:80>

  ServerName external.mywebsite.com

  <Location "/">
          Satisfy any
          require valid-user
          order allow,deny
          Allow from all
  </Location>


  ProxyRequests off
  ProxyPreserveHost on

  ProxyPass / http://localhost:8080/
  ProxyPassReverse / http://localhost:8080/

  <Proxy *>
          Order deny,allow
          Allow from all
          AuthType Basic
          AuthName "Private"
          AuthBasicProvider file
          AuthUserFile /path/to/htpasswd
          Require valid-user
  </Proxy>
</VirtualHost>

This works in as much that browsing to external.mydomain.com outputs from the backend. So the proxy itself is working, but it's as if the Auth directives are being ignored. I also tried moving the Auth directives into the <location> block, but this has the exact same effect.

I am using Apache2 v2.2.22 running on Ubuntu 12.04. Any suggestions?