How to unlock an icloud account, if the only reset option is an email to your icloud account?

My mum has a iPhone 5 which is locked to her iCloud account she is clearing it to allow it to be recycled but it is asking to login to her iCloud account.

But her iCloud account is locked and the only method left to reset and unlock is for instructions to be sent to her iCloud email address.

This phone which has already been hardware reset was the only device associated with the account. We have tried to log in with other devices but can't seem to find a way to login as it just says locked account and then proceeds to send another email to her iCloud email.

Its starting to sound like the account is lost and i should just introduce the phone to a sledge hammer and send it to scrapped / recycled.