User deletion of mailbox email addresses is not currently possible but you can give instructions for mailbox deletion to the TalkTalk Data Protection Office team. You'll need to provide sufficient proof that you are the registered user of the email address.
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.
