So it's after you log in? Then it is just about linking your id to another email address. Do you not have a non-sky one? You would still be able to access your sky mail, even if you use another address to link your log in details.
Sky used to use usernames to sign in.
They recently gave you the opportunity to link your non-sky email address to your sky username so you can use either to sign in. i.e. I can now sing into my sky account using my gmail address.
If you gave sky an email address to use as a back up, try...