TalkTalk staff are not permitted to delete email addresses / mailboxes.
User deletion of mailbox email addresses is not currently possible either but you can give instructions for mailbox deletion to the TalkTalk Data Protection Office team. They will need to verify that you are the registered user of the email addresses.
See the GDPR help page item 'Your Right to be Forgotten / Right to Erasure '. There's a postal address, which in my view is the best way to contact the Data Protection team, but you can initiate a contact via any of the TalkTalk contact methods.
