If you're in a need for fast and simple solution to block certain senders directly on Exim mail server, you're in luck. Couple of weeks back I needed to blacklist a spammer on a relay mail server, so that I could take my time and carefully trace the origin server/script from where the spam was being sent.
Implementing sender blocklist is very simple. Just open Exim's configuration file - if you're using CentOS or RHEL, look no further than /etc/exim/exim.conf. On Debian based distributions Exim's configuration is split into multiple files, so the recommended way of reconfiguring Exim is with dpkg-reconfigure exim4-config.