They do not provide an open relay. You can only send email via smtp.ntlworld if you are using your own PC connected to the net via your NTL internet. You can, however, sign up to alternative email providers who offer a smtp service, and access them from your NTL internet service.
I don't know what limits, if any, they impose, but if they do I imagine they will be well within the normal limits for contacting all your friends, or members of a club or society you may be secretary of. After all, you're not trying to spam thousands of addresses are you, as that would breach your terms and conditions.
to the site by the way.