It may just be coincidence that NTL have stopped accepting emails from bigfoot.com and they are rolling out an anti-spam product/service.
If I send 2 emails to myself from my work mail system I receive the one sent to @ntlworld.com yet the one sent to @bigfoot.com never arrives, no reply, no response, no message, nada. If it was just me and it was occasional I would put it down to one of those things. Unfortunately it isn't. I know 3 other people who have NTL broadband and have had to make alternative arrangements.
Whether mail directed through bigfoot.com appears like it has been 'relayed', I don't know. All I can say is that mail sent to ....@bigfoot.com doesn't arrive for me and a few others.
