What's the last part of your email address? talktalk.net, lineone.net, tiscali.co.uk or another in the tiscali family?
If one of the above, sign in to TalkTalk Mail here and Compose and send the same mailbox address a message so you can check the message sends and appears in the Sent objects folder and also arrives and stays in the Inbox.
If you get an error message let us know what that is.
How do you normally send emails? Via your computer or phone and do you get any error message that tells you why the send didn't happen?