When I go into Mail I get this message:
Your e-mail account *****@talktalk.net was disabled due to invalid credentials. Please edit the account and enter correct credentials to enable it again.
How can I get rid of this old account or stop receiving this message
You're presumably signed into a TalkTalk mailbox. I'll call that the primary mailbox.
The error message is presumably about an added email account. I'll call that the secondary mailbox.
If you wish to remove the secondary mailbox from the primary mailbox just select the dustbin icon to the right of the secondary mailbox and then confirm Delete account. This action just removes the secondary mailbox from the primary mailbox but does not delete the account.
However, the email address you posted, is showing as not valid on the system. If you've deleted it from your MyAccount then just follow the above advice to remove this secondary mailbox from the primary mailbox.
If you haven't deleted the secondary mailbox from your MyAccount then let us know what error message you see when trying to sign in directly to the secondary mailbox.
Let us know how you get on.