My iPhone kept defaulting to POP (@btinternet) although I wanted IMAP to see what was on the server.
There was no sign of IMAP on my phone.
But i've sussed it and here's how to do it for all those frustrated trying to get IMAP with btinternet.
First delete your name@btinternet account. Beware, you'll loose your emails. Back them up in folders on the server.
Now go to settings, mail, contacts, calendars and tap 'Add Account'. Tap 'Other' and tap 'Add Mail Account'.
Type in your details as normal but put in the wrong password. The server will fail to verify your account but magically up comes the IMAP tab and now tap it. Now correct your password and continue. The server still can't verify because your ports settings are wrong so keep trying until your phone allows you to save the setting.
Now go back to 'settings' mail, contacts, calendarsand make sure SSL is on for both incoming and outgoing servers.
The ports numbers should be changed to incoming 993 and outgoing SMTP 465.
Mine works a treat and I can see all the folders on the server.
Be careful how many times you try the wrong password, it may compromise your email account and if you log on online you may be asked to change your password.
Or you could try this:
Delete the account you want to change from POP to IMAP
Put the iPhone into Flight Mode so that it doesn't automatically set up the POP account.
Create the new account and enter the settings
Server incoming and out going: mail.btinternet.com
Incoming Port: 993 SSL security
Outgoing Port: 465 SSL security
Once the IMAP settings are entered remove Flight Mode.
During the set up process you will probably get a few messages complaining that your iPhone can't connect to your email server.
Just ignore these
Flight mode is just switching off the wireless which is preventing it from connecting and making the POP account which is basically what you are doing by entering the wrong password.