Can someone advise how to block or prevent this? illegalwebsite.com is hiding behind Cloudflare, so I cannot see their host IP.

If you go to Dashboard > Websites > Add a domain as if you would add a domain for your self, and you place there the "illegalwebsite.com" domain, Cloudflare will show you the A record with the IP address (I know, is weird, but that's how it works CF, even with our domains) along with all the other records. You can move from there to understand what is going on.

Ciao!