If you're asking about moving the existing email messages from your TalkTalk Inbox to a new Hotmail Inbox then the easiest way is to have both TalkTalk and Hotmail set up as IMAP email accounts in an email client like New Outlook for Windows or Thunderbird, for example, and just drag and drop the messages from one Inbox to the other.
Whilst your TalkTalk mailbox remains active you can collect your messages from the TalkTalk Inbox or forward them to Hotmail. Auto forwarding isn't reliable for all messages because that doesn't necessarily retain the required message authentication to prove the message is genuine and not spoofed or spam.
When you've notified your contacts of the new hotmail email address and they are regularly using that new email address you can ask the TalkTalk Data Protection team to delete your TalkTalk mailbox to protect your future security.
If I've misunderstood what you expect to be able to do then do please give some more detail on what you would like to achieve.
