It is probably a BT server problem. The best advice when it happens is to do nothing, especially do not change passwords or delete the account from your phone as that can cause more problems than it solves and it often resolves its self in a day or two.
The first thing to do when it happens is check to see if you can log on to your email account via a web browser. As you can there is obviously nothing wrong with your password or account hence the advice to do nothing.
You should then try turning off your BT Hub for about half an hour and when you turn it back on you will most likely have been issued a new IP address and connected to a different BT email server which may resolve the problem.
If the problem did not resolve its self you could try changing your password to see if it will resynchronise with the BT Mail server.
You should stop your iPhone and iPad and any other devices from checking for email. The easiest way of doing that is to turn them off if you still have the account on your device or in the settings add a couple of characters to the email address so that it is not checking your account.
Once you have done that, change your email password and check that you can access your email via webmail (on a browser).
If that works you should wait at least an hour to allow the servers to sync and then add the new password to your iPhone, remembering to remove any characters you may have added and again check it works. If it does then move onto the next device.
When entering the settings, make sure that in the Outgoing server you do not use the "use same as incoming" for the email address and password. Enter them manually.
If the above does not resolve the problem, when you change your BT password on an iPhone/iPad/Apple device it may only change for INCOMING mail.
To change the outgoing mail password you have to go into Settings; then scroll down to Passwords & Accounts or on older devices Mail, Contacts, Calendars. From there select the BT email account and select the account where it is listed under IMAP.
You will find the details for the account and can change the password for the Incoming server there, the outgoing mail server only shows SMTP and mail.btinternet.com You have to tap on that Primary Server in order to find where the Outgoing password is hidden so you can update it.
When setting up the email account on your device you are best to set it up manually, using "other" and ensure that you are using the correct settings as per the following link.
The default setting for the iPad account seems to be as a POP3 account. If you are wanting to set up as an IMAP account you may have to enter an incorrect password to cause the iPhone to reject the set up and it will then offer a choice of setting up as an IMAP or POP3 account.
https://www.bt.com/help/email/manage-email-account/manual-settings/what-are-the-settings-for-outgoin...
