Turns out it was not as easy as it may seem. This page describes things to do in your Linux host.

Install apache2 with mod_proxy, mod_proxy_html and mod_proxy_http (installed by default in Raspbian)

Enable mod_rewrite, mod_cache, mod_proxy, mod_proxy_http, mod_proxy_html (e.g. using a2enmod rewrite cache proxy proxy_http proxy_html)

Use a2ensite.

Throttle the Apache server to match to ITS server:

# ITS can really only handle one connection at a time!
MaxRequestsPerChild 1
ThreadsPerChild 1
MaxClients 1

Basic VirtualHost stuff:

<VirtualHost *:80>
  ServerAdmin victor@up.update.uu.se
  ServerSignature off
  ProxyRequests off
  ServerName up.update.uu.se
  ProxyPreserveHost On

  ErrorLog ${APACHE_LOG_DIR}/up-error.log
  CustomLog ${APACHE_LOG_DIR}/up-access.log combined
  LogLevel error

Optional: error documents for when the ITS server fails/crashes:

  Alias /its-error/ "/home/klh10/its/apache-errors/"
  ProxyPass /its-error/ !
  ProxyErrorOverride on
  ErrorDocument 503 /its-error/503.html
  ErrorDocument 404 /its-error/404.html

Optional(?): caching

  CacheEnable disk /

Optional: avoid robots which don't seem to respect robots.txt

  # Forbid the darn Baidu robot which doesn't respect robots.txt! And the Page2RSS thing which also doesn't, and connects every 2 minutes
  RewriteEngine on
  RewriteCond %{HTTP_USER_AGENT} ^.*Baiduspider [NC,OR]
  RewriteCond %{HTTP_USER_AGENT} ^.*Page2RSS [NC]
  RewriteRule .* - [L,F]

The real stuff: the proxy

  <Location />
    ProxyPass http://its-up.update.uu.se/ nocanon max=1 disablereuse=on retry=0 timeout=10 connectiontimeout=5
    ProxyPassReverse http://its-up.update.uu.se/
    # ITS only handles HTTP 1.0 and no keepalive
    SetEnv force-proxy-request-1.0 1
    SetEnv proxy-nokeepalive 1
    Order allow,deny
    Allow from all
  </Location>