If you need to change the IP that is used to send email out of your system, you can do so by editing your /etc/exim.conf.

Change:

remote_smtp:
  driver = smtp

to:

remote_smtp:
  driver = smtp
  interface = 1.2.3.4

You will also need to add "interface = 1.2.3.4" under the header dk_remote_smtp:

Like this:

dk_remote_smtp:
  driver = smtp
  interface = 1.2.3.4

Where 1.2.3.4 is the IP you want exim to use.