[exim] relay_hosts

A server, not within our network needs to be able to send mail from one
of our local exim domains to the same domain. I've got the following
config, and included the rule it appears to be failing on.

hostlist relay_hosts = ip : ip : ip-of-external-server

hostlist rroom_senders = +relay_hosts

  deny    hosts = !+rroom_senders
          domains = +rroom_domains : etc
          sender_domains = +rroom_domains : etc
          delay = 30s
          message = Your host is not authorised to send mail from
Reading Room group

Can anyone suggest why emails sent from the external machine are beign
refused when they come into our mail server?

Thanks!

John