Yes, change the name servers to win23.eukdns.com and win24.eukdns.com at your registrar (123reg) end so that your domains will start resolving from our name server and will point to eukhost server.
You can verify new name server using any DNS tool.
Traceroute, Ping, Domain Name Server (DNS) Lookup, WHOIS, and DNS Records Lookup
Matthew,
UK Web Hosting - Cheap Windows Linux cPanel Shared Reseller Web Hosting in UK