e-mails sent, but not being received.

Hi Nigel, you will not get a definitive answer unless you provide some details.
1/ what email client are you using ?? Outlook Thunderbird, Gmail etc.
2/ what OS are you using ?? windows XP or 7 or 8, Mac, ubuntu, etc.
3/ what ISP are you using ???
4/ what firewall
5/ what anti virus ???
6/ Have you run malware and anti virus scans recently?
etc.

As you can see there are a lot of information needed to start diagnostics.