How to delete an iCloud account you don't have access to

I've just upgraded the new iOS (on an iPhone 6 Plus) and it keeps continually asking for my iCloud login - over and over and over again! The problem is I don't have access to the email linked to this iCloud account - so when trying to reset the password I cannot use the 'recieve an email' option, nor can I remember the answers to the security questions. So I have absolutely no way of accessing this email or reseting the password via security questions. Is there a way I can have the account deleted off my iPhone? (It also asks for the password when I try to sign out..)