If you look at section 2.4 of the Terms and Conditions it says if you leave you can't keep the email account or email address.
Your MyAccount login will remain active for 12 months after you leave. You'll be able to continue to manage your email account there for at least 12 months.
My understanding is that your TalkTalk email will remain active so long as you use it at least once every 180 days and, whilst it does, the account / password recovery will also remain active.
You'll be able to use TalkTalk webmail whichever network you're moving to.
Other networks may not allow you to send TalkTalk mail via an email client.
After 12 months if you have need to change the email password then just come back here and ask but try the password recovery first.
In any event, it would be wise to set up an alternate email account, for example, a gMail or Yahoo account that's not with an ISP so that you've always got a backup not directly tied to any Broadband service.