Cannot add email account to iPhone

I recently migrated my official email account from one Exchange server to another. I deleted the old account on my iPhone, thinking I would be able to add the new one.

I go to Settings>Mail>Accounts>Add Account>Microsoft Exchange

The next screen does not ask for a password, only the address and a description. I enter the address and click Next. In the popup, I click "Sign In". (Actually, it doesn't matter which option I select.) After this, I see "Verifying" status for a couple of seconds but then get shunted back to the previous screen, i.e. the one where you select the type of account. I never get past this point. I am never prompted for a password.

The only other clue I have is that the same address is used for my iCloud account and is the official address for this phone. However, this has always been the case.

Any help appreciated.