There is a current problem with some incoming off-platform mail not being received or received delayed to talktalk.net mailboxes but using TalkTalk Mail webmail you should be good to send out mail messages.
When the MX servers (they're the ones receiving and forwarding mail to the TalkTalk Mail platform) are working normally then full service will resume.
The TalkTalk MX servers are responding normally and off-platform mail is being received into talktalk.net mailboxes as normal from around 9am this morning.
Any mail that was accepted for delivery and buffered will be received.
Otherwise senders will have received "Unable to deliver message after multiple retries" fail to deliver messages so they'll know their sent mail didn't get through.
Let us know if you're still experiencing email issues.