I have phoned NTL - there is an ongoing problem with outgoing outboud email.  You should be able to access your mail @ webmail.ntlworld.com - spooky though - that actaully works - which surprised me!  
Also - they are in the middle of a major upgrade - which should be finished  on the 18th.  (Don't think that upgrade is affect the current mail issue though).
Does that tesco smtp thing work then?  How?   I thought you would need to have some sort of authentication?
*Edit*  - Just changed my smtp address to mail.tecso.net - still not sending!