Can you send a message with links or attachments to yourself? If you can, it probably means some of your recipients are blocking your messages at their end, either through the antispam controls of their mail provider, or some security/antivirus app on their computer. Have the recipients checked the Spam/Bulk folders in their accounts?

Thank you, good suggestion.

I've just tried it and it failed. I also turned off my firewall for a few minutes and tried again - same result.

I just don't know where to look next!

I doubt the firewall affects it, but the antivirus could, or more likely your own mail provider is filtering messages with links or attachments, just as I suggested could be happening with your recipients. When it 'fails', is there not some error message or indication? If sent messages appear in Sent, they are at least reaching the mail server. Access the account in webmail to look for clues.

Aha! I accessed the account using webmail, as you suggested, and found the missing messsages in a Junk folder. This presumably means my mail provider has suddenly changed their spam filter rules...and I need to take it up with them.

I do feel relieved that the messages have not just disappeared into the great bit-bucket in the sky!

Thanks for your help.