That was the trick!
Sorry to overlook the documentation that was staring me in the face. If
it had been a snake, it would have bit me.
Thanks for your help.
> > deny hosts = partial-lsearch;/etc/exim/blocked-hosts
> > deny hosts = lsearch;/etc/exim/blocked-ip
>
> Those will search using the host name. If you want to search
> using the IP address, use net-lsearch. If you want to search
> using CIDR blocks as keys, use (e.g.) net24-lsearch. See
> section 10.9 (last two bullets).
>