Ok, let’s say you have fallen victim to spam scripts, or mass mailing from your server and you are blacklisted. Please note this is not a permanent fix to your underlying problem, but this will get mail delivering again.

On the other hand, if you just like to blow out you ISP’s IP addresses this will let you too I guess.

And here we go!
Find exim.conf, usually /etc/exim.conf

now look for the following lines:

remote_smtp:
  driver = smtp
  interface = ${if exists {/etc/mailips}{${lookup{$sender_address_domain}lsearch{/etc/mailips}{$value}{}}}{}}

AND

dk_remote_smtp:
  driver = smtp
  interface = ${if exists {/etc/mailips}{${lookup{$sender_address_domain}lsearch{/etc/mailips}{$value}{}}}{}}

Now what I want you to do is remove anything after interface =, so remove

 ${if exists {/etc/mailips}{${lookup{$sender_address_domain}lsearch{/etc/mailips}{$value}{}}}{}}

After this add your IP address.

Not done yet!
do the following

chattr +ia /etc/exim.conf
service exim restart

That will help it from not reverting back to your previous settings once a upcp of eximup is performed.

Hope this helps!