First of all to every wonderful being that posts their questions here. YOU ARE NOT in the same situation as original poster. While instructions that Winston (THANK YOU) posted were relevant back then in 2013 they are practically unnecessary now. Back then when IOS 7 was new in order to delete icloud account that was the SAME account, but RENAMED user name- his instruction to temporary change apple id email and sign out actually worked. NOW it is only needed once out of 1000 cases, cause IOS 8 and 9 allow to sign out of icloud with correct password, but new or old email at the top of the screen(as long as it is the same account). People who come here and think their question is the SAME are wrong. While I understand that it feels like if you post here response will be good, response will be wrong, cause your situation is JUST DIFFERENT.
Hence Winston gives you different answer. So answer to everyone, create your own thread. Explain YOUR Personal situation.
Specifically to Orange. Your answer will depend on the simple fact which situation is correct?
1. Your work email was your actual apple id and now your are using different apple id.
2. Your work email was your current apple id and you still using the same id, but changed your primary email.
If it is number 2 - just use your current password to sign out of icloud
if and I am pretty sure it is number 1 use last Winston's boilerplate above.
And if you already tried and failed to verify yourself with apple support, simply contact the place where you got that phone and ask for copy of the receipt.
They (apple support) help with consumer receipts as well.