Sign in to TalkTalk Mail webmail (desktop browser) and select in the List view the mail messages you wish to save. When selected via the tick boxes the Toolbar will appear immediately below the header and to the right of the toolbar icons will be a triple dots (ellipsis) icon for More actions. The menu for More actions has a Save as file option. That will save a single message in eml format the standard email file format. Multiple messages will be in eml format but zipped up in zip file format.
Outlook* doesn't natively support eml files. Just connect your Outlook email client to your TalkTalk mailbox as an IMAP account connection and you'll see all your mail messages. Backup messages from Outlook.
*New Outlook for Windows does support eml files and you can save direct from that new Outlook software.
