I need exim to send all outbound email through a remote mail server

If you need to send all outbound mail through another smtp server (example, if your ISP blocks your port 25 and you have no other way of sending mail) you can do so by editing your /etc/exim.conf and changing:

lookuphost:
  driver = dnslookup
  domains = ! +local_domains
  ignore_target_hosts = 127.0.0.0/8
  condition = "${perl{check_limits}}"
  transport = remote_smtp
  no_more

to

smart_route:
  driver = manualroute
  domains = ! +local_domains
  ignore_target_hosts = 127.0.0.0/8
  condition = "${perl{check_limits}}"
  transport = remote_smtp
  route_list = * smtp.yourisp.com
  no_more

Where smtp.yourisp.com is the server you want to send your mail though.

Restart exim after making changes to your exim.conf