Neither of the two things you were told were correct- If you old account is disconnected, the email account will now have been closed, but it is still "attached" to that account in the billing system.
You can get the email address back, but the process is rather complicated- Ntl need to reconnect the old account, reactivate the email accounts, then speak to both yourself and your parents at the same time to conform with the Data Protection Act.... The addresses can then be migrated to your parents account and they will remain active as long as that account does. Your old account can then be fully disconnected again.
Confused yet?!
The problem you have is that your chances of phoning ntl and getting someone who knows how to and has the access to do this are quite slim... good luck if you try though!!