Why would I ever want to change to something else?
Because of the issues you've just been explaining!
Register your own domain name with 1&1 or another suitable domain provider, you can then setup up as many email addresses as you want such as [email protected], but set these to forward to your current ISP email addresses.
Minimal cost and you are very unlikely to lose the domain and can easily change the addresses they forward to with no need to change the main email address.
This is what I've done and when I change ISP to Virgin next year after 14 years with Plusnet, I can just change the forwarding address and the IMAP stuff in our email clients.
In your situation though I'd do the above going forward, then if/when the NTL address is lost at least all your new contacts/registrations will be to the new address.