If Outlook and if other email apps are working and the problem is only apparent when using Mail it would tend to point to a problem with either Mail or its settings. If it was a BT server problem it is doubtful that any email app would work for you.
When setting up an email client it is best to do it manually, entering all the settings correctly rather than using the "wizard".
In case you are unaware how to set up the email account manually:-
When you set up Mail on iphones in order to get to the manual settings you need to set up your email account with the wrong email address or password. This will cause a failure of the account authenticating and it will open up the manual settings.
You can then select to set up as an IMAP or POP3 account and you can enter all the correct settings, including the correct email address and password, and tick the correct boxes as per the BT settings in this link.
http://bt.custhelp.com/app/answers/detail/a_id/44917/kw/bt%20mail/c/346,6588,6591
EDIT: For the purposes of testing you can set up Mail as well as Outlook or any other email app on the same iphone at the same time so you do not need to delete Outlook in order to try another email app.
